Brown, reeling after a chaotic week in which ministers resigned amid disastrous local elections, is facing intense public anger over a deep recession and the escalating row over lawmakers’ expenses.
Pressure mounted on Sunday ahead of results from the European Parliament elections in which polls suggest Labour could come third or even fourth, with the main opposition Conservatives in the lead.
Results from the elections held across the 27-nation bloc are expected after 2000 GMT.
Fringe parties in Britain, such as the anti-European UK Independence Party (Ukip) and the far-right British National Party (BNP), are also forecast to benefit from voter anger at Labour, which has been in power since 1997.
General election
Business Secretary Peter Mandelson warned party rebels that any attempt to replace Brown would spark a general election.
“If we were to have a third leader in a single parliament it would mean irresistible pressure to hold a general election before we were able to carry out the changes in the economy, and public services, and Westminster, that people want to see from us,” the Business Secretary said.