David Cameron has said the government has a “fundamental responsibility to bring our country together” in the aftermath of the EU referendum.
He told MPs that negotiating an exit would be the civil service’s most complex and important task for decades.
Allies of Jeremy Corbyn have insisted he will not resign in the wake of the Brexit vote, accusing MPs seeking to depose him of “subverting” democracy.
The Labour leader faces a motion of no confidence in him on Tuesday.
A secret ballot on Mr Corbyn’s leadership will be held after nearly 40 of his shadow ministerial team resigned.
The result, however, will not be binding on the Labour leader and allies of Mr Corbyn has insisted he will stand in any subsequent leadership election if an alternative candidate puts themselves forward.
UK financial markets have remained volatile in the wake of the Brexit vote, with sterling plunging to a 31-year low against the dollar, and some share trading temporarily halted.
The UK has also lost its AAA credit rating after it was downgraded by Standard and Poor’s. The country was also downgraded from AA+ to AA with a negative outlook by ratings agency Fitch.
EU leaders say they will not hold informal talks with the UK until it officially notifies them of its exit.
Mr Cameron is to stand down as prime minister by October, and has triggered a Conservative leadership contest, while Mr Corbyn is facing a revolt in his shadow cabinet with members questioning his performance in the referendum campaign.
The PM told MPs he did not take back the warnings he made during the campaign about the consequences of leaving the EU, saying it would be “difficult” with “challenging new negotiations” ahead.
While “all of the key decisions” would wait for his successor, he said there was work to be done in the meantime, and a new EU unit had been set up in Whitehall to “bring together expertise”.
He defended the decision to call the referendum, saying MPs had backed it by a margin of six to one, and said the Scottish, Welsh and Northern Irish governments would be “fully involved” in the negotiations.
He also condemned “despicable” racist attacks that have been reported since the referendum result, saying they must be stamped out.
Mr Corbyn has been accused of lukewarm support for – and his office of actively trying to undermine – Labour’s campaign to remain in the EU. He took to the despatch box amid a mass resignation of members of his shadow cabinet.
In a message for the critics in his own party – more than 30 of which have resigned in the past 36 hours – he said: “Our country is divided and the country will thank neither the benches in front of me nor those behind me (where Labour MPs sit) for indulging in internal factional manoeuvring at this time.”
Mr Corbyn said the outcome of the referendum showed “many people feel disenfranchised and powerless”, saying communities had been “let down, not by the European Union but by the Tory government”.
He called for reassurances that levels of EU funding that had been pledged would be protected, and attacked the Leave campaign which he said had “made claims they knew to be false”.
Lib Dem leader Tim Farron said he would continue fighting for the UK to remain a member of the EU, while the SNP’s Angus Robertson said his party had “no intention whatsoever of seeing Scotland taken out of Europe”.
Scotland voted overall for Remain, and the Scottish government has suggested a second independence referendum could be needed to retain its status in the EU.
After a meeting with German Chancellor Angela Merkel in Berlin, French President Francois Hollande and Italian Prime Minister Matteo Renzi emphasised the need to process the UK’s exit as quickly as possible and focus on the challenges facing the remaining 27 states.