Gordon Brown has insisted Labour could still win the general election outright as another poll showed the Tory lead narrowing.
Research by ICM for the Sunday Telegraph put David Cameron's party down one point since last month on 39%.
Labour were unchanged on 30%, while the Lib Dems were up two on 20%.
It is the first ICM poll to have Conservative support below 40% since last June, at the height of the MPs' expenses scandal.
The findings - which would result in a hung parliament with Mr Cameron around 14 seats short of an overall majority - come amid speculation that the Prime Minister could choose to go to the country earlier than the widely anticipated date of May 6.
A senior Labour source told the Sunday Telegraph: "May is still the favourite but you certainly shouldn't rule April out."
In an interview with the Observer, Mr Brown said he still believed he could secure an overall majority despite the long-term poll deficit.
"I'm not complacent, but Labour can still win it," he said. "I'm absolutely sure of that."
:: ICM interviewed a random sample of 1,001 adults by telephone on February 3 and 4. The results were weighted to the profile of the UK population.