David Cameron accused Ed Miliband of siding with Russia and letting down the United States over Syria in an acrimonious phone call made between the leaders a day before the Commons votes against intervention in Syria, according to Labour sources.

Details of the remarkably frank conversation emerged after Downing Street aides attempted to blame Miliband for killing off the government's plans to take military action against Bashar al-Assad's regime in conjunction with the US.

When Miliband made it clear in the call he would not support the government motion without more conditions, an exasperated Cameron accused him of "letting down America" and "siding with [Sergei] Lavrov", the Russian foreign minister, and an ally of Assad.

One Labour aide said that was the point in which negotiations between Cameron and Miliband first started to break down on Wednesday.

Cameron was hoping to reach cross-party consensus on a roadmap towards military action.

The Labour source said Miliband had also been disappointed by the language of a government source, who told the Times: "No 10 and the Foreign Office think Miliband is a fucking cunt and a copper-bottomed shit."

"Ed wasn't angry, he was frustrated by the flippancy of it," the Labour source said.

Relations between Downing Street and Labour have grown increasingly bitter over the last 48 hours, as the two sides failed to back a common motion on Syria.

No 10 sources said Miliband had previously signalled he would support military intervention in Syria and only withdrew at the 11th hour to demand more time for weapons inspectors, more involvement of the UN and a second vote before committing military forces.

However, Labour sources insist Miliband never agreed to back the prime minister and had simply agreed to go away to consult with colleagues about the proposals.

Asked on Friday whether he felt betrayed by Miliband's decision to withdraw his support, Cameron said it was a matter for the Labour leader to "defend the way he behaved and his conduct".

In an interview with Sky News, he also said the government will still seek a "robust response" to Syria after MPs rejected the prospect of missile strikes on the regime.

He said British plans to join America in a military campaign "won't be happening" but there were other ways of "upholding the international taboo on the use of chemical weapons".

Cameron has not spoken to Barack Obama, who is planning to press on alone with strikes, but felt there was "no question of having to apologise" to Britain's closest ally.

He told Sky News he believed Obama and the America public would understand that he had to listen to parliament, which "reflected the great scepticism of the British people".

The public unease about getting involved in another Middle East war "trumped the sense of outrage about chemical weapons", he added.

He insisted Britain was still "deeply engaged in the world" and argued the rejection of military action "doesn't stop us working with allies to bring maximum pressure on the regime" through the UN and other international bodies.

Cameron also contrasted his willingness to listen to parliament "very, very clearly" with Tony Blair's approach in the runup to the Iraq war in 2003.

The coalition lost the vote after Labour decided it would join with 39 Tory and Liberal Democrat rebels in rejecting the government's general motion proposing military action against Syria "if necessary".

The prime minister said he had forgiven two Tory ministers who missed the tight vote – Justine Greening, the international development secretary, and Mark Simmonds, a junior Foreign Office minister – who both claimed not to have heard the division bell.

"This was a technical issue," he said. "They have apologised profoundly and I've accepted their apology."

Earlier, the prime minister was defended by his chancellor, George Osborne, for trying to seek a consensus.

However, the senior Tory also warned that Britain would have to do some "soul-searching" about its international role, saying he hoped this was not "the moment where we turn our back on the world's problems".

Speaking on BBC Radio 4's Today programme, he acknowledged it could place a strain on the "special relationship" between Britain and the US.

"I think there will be a national soul-searching about our role in the world and whether Britain wants to play a big part in upholding the international system, be that a big open and trading nation that I'd like us to be or whether we turn our back on that," he said.

"I understand the deep scepticism that my colleagues in parliament and many members of the public have about British involvement in Syria.

"I hope this doesn't become the moment where we turn our back on the world's problems."