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Senior Labour MPs are taking soundings as the party begins its search for a new leader.
The ruling National Executive Committee will meet early next week to agree a timetable for the contest to replace Ed Miliband.
Yvette Cooper, Andy Burnham and Chuka Umunna are seen as the frontrunners.
A separate contest will also be needed to chose a deputy party leader.
Conservative Prime Minister David Cameron has promised to lead a government for “one nation” after his party won its first majority since 1992 with 331 seats.
Labour ended up with 232 MPs, sustaining heavy losses at the hands of the SNP in Scotland and failing to make significant gains elsewhere.
In other election developments:
Mr Cameron is finalising his first all-Conservative cabinet
- Tim Farron said he would decide “in the next few days” whether to put himself forward to replace Nick Clegg as Lib Dem leader
- Anti-austerity protests are taking place outside Downing Street and in Cardiff
- The Unite union, Labour’s biggest donor during the last parliament,called for its leader in Scotland, Jim Murphy, to resign
- SNP leader Nicola Sturgeon has met all her party’s 56 new MPs in Edinburgh after they swept the board in Scotland
- The Conservatives have also made gains in council elections in England, gaining more than 500 seats
- Watch BBC election coverage and follow latest reaction
- Read more analysis from the BBC’s experts
- Find your constituency’s result
BBC political correspondent Iain Watson said Mr Burnham, the shadow health secretary, and Mr Umunna, the shadow business secretary, were believed to be taking soundings before declaring their bids to become leader.
Ms Cooper, the shadow home secretary, shadow health minister Liz Kendall and former soldier Dan Jarvis are also likely to consider a bid, he added.