Foreign Secretary Margaret Beckett has arrived in Iraq for a surprise visit as controversy goes on over UK deployments there and in Afghanistan.
The handover of security responsibility in Iraq from British to local forces will continue, UK Foreign Secretary Margaret Beckett has said.
The new head of the Army, General Sir Richard Dannatt, has warned that his soldiers can "just" cope with the demands placed on them by ministers.
Mrs Beckett, in Iraq on a fact-finding mission, met the country's Deputy Prime Minister, Barham Saleh, in Baghdad.
Tony Blair has said the UK must "stand firm" against global terrorism threat.
Afterwards, she said it was "absolutely key" that the elected Iraqi government was seen to be taking responsibility.
His words came after one soldier was killed in Kabul and two died in a bomb attack near Basra, in southern Iraq.
Meanwhile, Iraq's parliament has voted to extend the country's state of emergency for a further 30 days.
The latest military casualties follow the deaths of 14 servicemen killed when their Nimrod MR2 aircraft came down in Afghanistan on Saturday.
The measure, which has been in place for two years, allows for night-time curfews and gives the authorities extra powers, including the ability to make arrests without warrants.
Mrs Beckett is making her first visit to Iraq since she took office and plans to meet Iraqi Prime Minister Nouri Maliki as well as other politicians.
Britain transferred control of Muthana province in July and Dhi Qar is expected to follow this month.
"While security and the political process tops our agenda, I will also be discussing the other challenges before the Iraqi government," she said.
This would leave only Basra and Maysan provinces in British hands.
"The economy suffered decades of under-investment and mismanagement by Saddam's brutal regime which have left the Iraqis with a huge challenge."
This is an enduring partnership to defeat terrorism Barham Saleh
After the deaths, Mr Blair said: "It's so important for us to make sure we stand firm in Afghanistan and stop that country being a training ground for the export of terrorism around the world."
Mrs Beckett said: "There has been responsibility that has been transferred already, we hope and believe that that is a process that will continue."
The two British soldiers killed near Basra on Monday were part of a patrol targeted by a roadside bomb and small arms fire near the town of Ad Dayr at about 1300 local time.
She said it was "vital to the future of the people of Iraq that this government succeeds, because there will certainly never be a better chance to rebuild a better Iraq".
Another two soldiers were injured - one seriously - and have been taken to the Shaibah Logistics Base by helicopter for emergency medical treatment.
Mr Saleh said Iraqis would be "increasingly in the lead" as far as security was concerned.
"But this is an enduring partnership to defeat terrorism," he added.
The Ministry of Defence said the British soldier killed in the suicide bombing in Kabul on Monday was from the Argyll and Sutherland Highlanders, 5th Battalion Royal Regiment of Scotland.
Mrs Beckett is making her first visit to Iraq since taking office.
A further three soldiers were injured.
She is due to meet Prime Minister Nouri Maliki later and said she would not be limited to talking about the security situation, and intended to tackle issues such as the country's economy.
The latest fatalities bring the death toll of UK forces personnel in Afghanistan to 37 since the start of operations in November 2001.
Shortly after meeting Mrs Beckett, Mr Saleh left on a visit to Iran to develop ties with Tehran ahead of a planned visit there by Mr Maliki.
Senior Conservative MP Sir Peter Tapsell told the BBC that British forces were involved in a battle which could not be won.
"We couldn't do the job if we had a 100,000 men there."
