The move comes after Liberal Democrat leader Tim Farron was forced to rule out any electoral pact despite Sir Vince Cable urging his party's supporters to back Labour candidates in key marginals.
Labour chief whip Nick Brown also ruled out a progressive alliance between the Greens, the Liberal Democrats and Labour.
"The way to defeat the Conservatives is for the Liberal Democrats and Greens to stand down and for voters to vote Labour," Brown told The Newcastle Chronicle.
But the Greens have decided not to contest the Tory marginal of Brighton Kemptown in a bid to help Labour.
The party is also not fielding a candidate in the Labour London marginal of Ealing in an effort to stop the seat going to the Conservatives.
Caroline Lucas, the Green co-leader and Brighton Pavilion candidate, had called for last-minute talks with Jeremy Corbyn to discuss a progressive alliance.
But she scrapped the plan after Labour suspended Surrey-based activist Steve Williams for advocating an alliance around a pro-NHS candidate to beat Tory Health Secretary Jeremy Hunt. "We're drawing a line under it," the senior source said.
The development comes just a month before the general election on 8 June. The latest ICM poll, of more than 2,000 voters between 5 and 7 May, put the Conservatives on 49%, Labour on 27%, the Liberal Democrats on 9% and the Greens on 3%.