Meanwhile, customers of the Icesave internet bank have been warned they will probably have to claim compensation for money held in their savings accounts.
UK authorities are preparing for the bank's parent in Iceland, Landsbanki, to be declared insolvent.
Icesave has 350,000 savers in the UK and Netherlands, with about £4.5bn of deposits.
A Downing Street spokesman declined to comment on whether there would be any House of Commons statement about Mr Brown's meeting.
Any announcements would be made in a "calm and orderly way", he said.
There was no mention of the talks at the lobby briefing for journalists earlier on Tuesday.
BBC political correspondent James Landale said: "Clearly things are moving. The question is 'how fast?'"
Monday's meeting was attended by Mr Darling, Mr King and Lord Turner, as well as representatives of RBS, Barclays and Lloyds TSB.
The Treasury is understood to have been formulating a plan that would allow the government to provide extra funding to the banks in exchange for stakes in them.
The government said it would not speculate about what policy options were being considered.