David Cameron insisted that he would not be apologising to US President Barack Obama after his humiliating Commons vote defeat last night meant the UK will not join a coalition in military action on Syria.

Speaking in Downing Street today, the Prime Minister admitted that “politics is difficult” and said: “I think the American people and President Obama will understand that.”

Mr Cameron has not spoken to the president since the failed vote that would have meant Britain could, in principle, have joined the Americans in air strikes on Syrian government targets, after a chemical attack on Damascus which has been blamed on the Bashar al-Assad regime.

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Ministers suggested the defeat in Parliament could put a strain on the special relationship with Washington, after the US specifically made a request for British help.

But the Prime Minister said: “I don't think it's a question of having to apologise.”

He said he would be speaking to Mr Obama “over the next day”, and that he had always wanted to act in “the right way” over Syria, meaning acting “as a democrat, in a different way to previous prime ministers and properly consult[ing] Parliament”.

Former Lib Dem leader and ex-special forces soldier Paddy Ashdown said earlier that he was “ashamed” of the MPs’ decision, which would “smash” the country’s relationship with the US and leave Britain “hugely diminished” on the world stage.

In spite of the vote, Mr Cameron said Britain would still be able to provide a “robust response” to the use of chemical weapons in Syria.

He said: “There are a series of things we will continue to do.

“We will continue to take a case to the United Nations, we will continue to work in all the organisations we are members of - whether the EU, or Nato, or the G8 or the G20 - to condemn what's happened in Syria.

"It's important we uphold the international taboo on the use of chemical weapons.

“But one thing that was proposed, the potential - only after another vote - involvement of the British military in any action, that won't be happening.”

He said the Government and Parliament would remain "deeply engaged in the world".

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Highlighting the UK's military power and diplomatic influence, he said: "We have great strengths as a country, we should continue to use those.

“But on this specific issue, because of the huge concerns about this appalling Syrian conflict and people worrying about how we might get sucked into it, on that specific issue that trumped, as it were, the sense of outrage about the chemical weapons.

"I understand that, I get that."

Meanwhile, AFP reported that Russia has welcomed the UK’s rejection of a Syria military strike, according to a Kremlin advisor.

And a BBC correspondent in Damascus said Syrian officials reacted similarly, with Dr Bassam Abu Abdullah from the regime’s Information Ministry claiming European countries had gone off the idea of action because they knew “the consequences would be too dire”.