And she told International Olympic Committee members at Buckingham Palace that hosting the Games had inspired "our children and communities".
He also said civil servants were among "pools of people" ready to step in if a planned strike by Border Agency staff at Heathrow goes ahead on Thursday.
She spoke ahead of an opening ceremony rehearsal, where the crowd was urged to to keep things "under wraps".
The culture secretary has said Games preparations are "on track".
Meanwhile, the PM's spokesman has said transport disruption during the Olympics is inevitable.
The news comes just three days before two Olympic matches - between Mexico and South Korea, and Gabon and Switzerland - are due to be held at the 50,000-plus capacity stadium.
It follows the drafting in of an extra 3,500 service personnel after G4S admitted a shortage of staff.
In other developments on Monday:
In other developments on Monday:
The Queen has welcomed members of the International Olympic Committee (IOC), including president Jacques Rogge, to London at a Buckingham Palace reception
Foreign sports fans have queued for hours to pick up Olympics tickets from reseller Cosport at its base in Paddington Green in London. Cosport was unavailable for comment
The White House announces that US First Lady Michelle Obama will travel to London to attend Friday's opening ceremony
A minute's silence is held at London's Olympic Village in memory of the 11 Israeli team members killed in the 1972 Munich Olympics massacre
Royal Mail says it will issue stamps honouring each Team GB gold medallist by noon the day after each individual athlete's win
Almost two-thirds of Team GB's athletes believe facilities for Olympic sports in the UK have improved as a result of London 2012, a BBC sport website survey suggests
Cyclist Sir Chris Hoy href="/sport/0/olympics/18953729" title="Hoy chosen as Team GB flagbearer" >has been chosen to carry the flag for Team GB at the London 2012 opening ceremony
The White House said US First Lady Michelle Obama would travel to London to attend Friday's opening ceremony
A minute's silence was held at London's Olympic Village in memory of the 11 Israeli team members killed in the 1972 Munich Olympics massacre
Royal Mail said it would issue stamps honouring each Team GB gold medallist by noon the day after each individual athlete's win
Almost two-thirds of Team GB's athletes believe facilities for Olympic sports in the UK have improved as a result of London 2012, a BBC sport website survey suggestsed
Up to 1,000 members of the Rail Maritime and Transport union at South West Trains will take industrial action - in the form of a work to rule - from Friday until 12 August in a row over a Games bonus payment
The prime minister's spokesman spoke after the first of a series of daily ministerial meetings - in the Cobra briefing room - to be held throughout the Games period.
The Queen, at a reception for IOC members in the palace's ballroom, said that, in the coming days, 10,000 athletes from more than 200 nations would be undertaking final preparations.
Transport, security and the threat of strikes were on the agenda for the first of the meetings, which was chaired by Prime Minister David Cameron and addressed by speakers including Transport Secretary Justine Greening.
"We send our warm wishes to them all for a rewarding and enjoyable Games," she added.
The meeting heard that the painting of lanes that make up the Olympic route network - stretching over 30 miles of London's roads - had been completed at the weekend and would become fully operational from Wednesday.
She said hosting the Games had inspired Britons "whether by motivating them to take up physical activity or encouraging them to demonstrate the Olympic values of excellence, respect and friendship".
Some Games lanes are already in place, including on the M4 from Heathrow into central London.
"Nowhere has this been more evident than in the warm welcome given to the Olympic torchbearers as the Olympic flame has travelled the length and breadth of the United Kingdom," she added.
The closure of lanes on the A40 near Wembley and the A12 and A13 near the Olympic Park on Monday morning - in preparation for Wednesday - meant drivers coming into London faced delays of up to two hours.
"The reality is that there is going to be disruption," Mr Cameron's spokesman said.
"The reality is that there is going to be disruption," David Cameron's spokesman said.
"We have huge numbers of people coming to London to enjoy the Olympic Games and that will put pressure on the transport system.
"We have huge numbers of people coming to London to enjoy the Olympic Games and that will put pressure on the transport system.
"We have been keen to stress that point, so that people who don't have to come into London don't come into London."
"We have been keen to stress that point, so that people who don't have to come into London don't come into London."
Meanwhile, members of the Public and Commercial Services (PCS) union who work at the Home Office will strike for 24 hours over job cuts and other issues on Thursday - the day before the Olympics begins.
He spoke after the first of a series of daily ministerial meetings - in the Cobra briefing room - to be held throughout the Games period.
Transport, security and the threat of strikes were on the agenda for the first of the meetings, which was chaired by Prime Minister David Cameron and addressed by speakers including Transport Secretary Justine Greening.
Members of the Public and Commercial Services (PCS) union who work at the Home Office will strike for 24 hours over job cuts and other issues on Thursday - the day before the Olympics begins.
Home Secretary Theresa May told the government meeting about contingency plans to try to cover striking workers, who will include Border Agency staff at Heathrow, and other airports on a day when many thousands of visitors are due to arrive in the UK.
Home Secretary Theresa May told the government meeting about contingency plans to try to cover striking workers, who will include Border Agency staff at Heathrow, and other airports on a day when many thousands of visitors are due to arrive in the UK.
The PCS said 57.2% of those who voted had backed strike action - the turnout was 20%.
The PCS said 57.2% of those who voted had backed strike action - the turnout was 20%.
The prime minister's spokesman said it was unclear how many workers would stay away on the day but there were enough people who had done the necessary training to step in to fill gaps.
The prime minister's spokesman said it was unclear how many workers would stay away on the day but there were enough people who had done the necessary training to step in to fill gaps.
"The PCS have been saying this strike is nothing to do with the Olympics," he said.
"Well, the strike is planned for later this week, and it's difficult for others not to see a connection there."
On security, he said "robust plans" were in place to try to ensure "a safe and secure Olympics".
On security, he said "robust plans" were in place to try to ensure "a safe and secure Olympics".
Meanwhile, IOC president Jacques Rogge told BBC Radio 4's Today programme on Monday the deployment of 3,500 extra servicemen and women to combat a shortage of security staff was "a good strategy".
That followed the drafting in of an extra 3,500 service personnel last week after contractor G4S admitted a shortage of staff.
International Olympic Committee president Jacques Rogge told BBC Radio 4's Today programme earlier that that deployment had been "a good strategy".
"They have found a solution, we are happy with it and we are very confident that security will be very, very good," he added.
"They have found a solution, we are happy with it and we are very confident that security will be very, very good," he added.
Culture Secretary Jeremy Hunt, meanwhile, said the transport system was "holding up well" and that Heathrow had worked "extremely well".
Meanwhile, foreign sports fans have queued for up to six hours to pick up Olympics tickets from reseller Cosport at its base in Paddington Green in London.
"We've got a third of the athletes now settled into the Olympic village and they like it a lot," he added.
The company, which sells Games tickets to people from countries including the US, Canada, Australia, Norway and Sweden, was also criticised for selling some batches of tickets to families with seats that were not together.
Meanwhile, up to 1,000 members of the Rail Maritime and Transport union at South West Trains are to take industrial action during the Olympics in a row over a Games bonus payment.
Cosport was unavailable for comment.
They rejected strike action but voted to work to rule, including a ban on overtime, from Friday, the day of the opening ceremony, to August 12, the last day of the Games.
Do you live in the areas that are hosting the Olympics? Have you faced any travel problems so far? How are you preparing for the Games? Send us your comments and experiences using the form below.
Do you live in the areas that are hosting the Olympics? Have you faced any travel problems so far? How are you preparing for the Games? Send us your comments and experiences using the form below.
