"The Bank of England and the banks agreed to continue their close dialogue with the objective of restoring more orderly market conditions," it said.
Angela Knight, chief executive of the British Bankers Association, told the BBC's Today programme that she was confident the Bank would take action.
The banks represented were HSBC, Royal Bank of Scotland, Barclays, Lloyds TSB and HBOS.
"The Bank of England is very keen to ensure that we have good strong confidence in our market - after all we've got good strong banks," she said.
HBOS shares were among the top gainers on the London Stock Exchange on Thursday, up 6.2% recovering most of their falls from the previous day.
"We're all facing as I say a particularly unusual situation in this credit crunch."
'No substance'
On Wednesday, the Financial Services Authority (FSA) said it would "not tolerate" traders starting "false" rumours about firms to make cash from dealing in their shares.
On Wednesday, the Financial Services Authority (FSA) said it would "not tolerate" traders starting "false" rumours about firms to make cash from dealing in their shares.
WHAT IS SHORT-SELLING? Trader borrows shares, then sells themRepurchases shares later at a lower priceTrader returns shares to lenderMakes a profit on the difference
HBOS, whose shares fell as much as 17% at one stage on Wednesday, denied rumours of funding difficulties.
"There has been a series of rumours in the market today [Wednesday]," said a HBOS spokesman.
"A number of ill-founded and malicious rumours about the UK banking system in the markets.
"These rumours have not a shred of substance whatsoever. They are lies."
'Just criminals'
HBOS said it supported the "decisive action" of the FSA to investigate the alleged market abuse.
Those behind the rumours are no worse than ordinary criminals, they're just basically stealing money from the market Banking analyst Ralph Silva
"There has been a series of completely unfounded rumours about UK financial institutions in the London market over the last few days, sometimes accompanied by short-selling," the FSA said in a statement.
In short-selling a trader borrows shares, sells them immediately and hopes to repurchase the shares in the future at a lower price.
The trader can then return them to the lender and make a profit on the difference.
Ralph Silva, a banking analyst at financial consultancy and research firm, Tower Group, told BBC Radio Five Live that those behind the false rumours "ought to be flogged".
"They're no worse than ordinary criminals, they're just basically stealing money from the market," he said.
"They're putting out rumours, they're putting out lies, and they're taking advantage of the lies they put out, they're just criminals."
The credit crunch started last summer following the revelation of multi-billion dollar bad debts in the US mortgage sector.
The knock-on impact has made banks around the world unwilling to lend to each other, making credit much harder to find and more expensive.