US President Barack Obama has said he fully respects David Cameron’s approach after Parliament blocked UK involvement in possible military action in Syria.
The men spoke by phone for 15 minutes, and the tone of the conversation was said to be friendly.
The UK prime minister reiterated he still wanted a strong response to the suspected chemical weapons attack.
According to Downing Street, Mr Obama said he had not yet decided what action the US would take over Syria.
A Downing Street spokesman said: “The prime minister made clear that he strongly believes in the need for a tough and robust response to the appalling war crime committed by the Assad regime in Ghouta.
“The PM explained that he wanted to build a consensual approach in Britain for our response and that the government had accepted the clear view of the House against British military action.
“President Obama said he fully respected the PM’s approach and that he had not yet taken a decision on the US response.”
Foreign Secretary William Hague said US Secretary of State John Kerry had thanked him for the UK’s “steadfast friendship”, and they were united on ending the Syria conflict and use of chemical weapons.
The White House believes President Bashar al-Assad’s regime was responsible for the chemical attack on 21 August which it says killed 1,429 people in the Ghouta suburb of Damascus – a figure far higher than previously reported.
“We know rockets came only from regime-controlled areas and landed only in opposition-held areas,” Mr Kerry said earlier.
“All of these things we know, the American intelligence community has high confidence.”
Ministers ruled out British involvement in any military action on Thursday evening after MPs blocked a government motion which called for military action if it was backed up by evidence from the UN weapons inspectors.
Despite the result of the vote, the US said it would continue to seek a coalition for military intervention, while France said the vote did not change its resolve about the need to act.
The president and prime minister agreed the US and UK would work closely together on a wider response to the Syrian crisis and try to find a solution.
Russia – which has close ties with the the government of Syrian President Bashar al-Assad – welcomed the UK’s rejection of a military strike, while Germany has ruled out participation in any action.
‘Whole region’ threatened
Meanwhile, Number 10 said it was “not too worried” by the absence of the UK from a roll call of allies in Mr Kerry’s speech earlier.
Mr Kerry made a point of describing France as America’s “oldest ally” while not mentioning the UK.
A Downing Street spokesman said: “The president stressed his appreciation of his strong friendship with the prime minister and of the strength, durability and depth of the special relationship between our two countries. They agreed that their co-operation on international issues would continue in the future.”
Mr Cameron said in an interview on Friday it was a “regret” that he had been unable to build a consensus on the response to the suspected chemical weapons attack.
However, he insisted the UK remained “deeply engaged” on the world stage.
The inspectors have finished their investigation and are expected to deliver their preliminary findings to UN secretary general Ban Ki-moon on Saturday.
Meanwhile in Syria, the BBC’s Middle East editor Jeremy Bowen said he had spoken to people inside President Assad’s administration who were “cock-a-hoop” at the UK vote. “They believe it counts as a victory for them,” he added.
“We will defend ourselves,” Dr Bassam Abu Abdullah from the Syrian Information Ministry said, warning of danger “not only on the Syrian people but… the whole region” if the US decided to attack.
But Mr Cameron vowed to “continue to take a case to the United Nations”, adding: “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.”
There had been suggestions from ministers, including Defence Secretary Phillip Hammond, that Britain’s rejection of military action would harm its relationship with the US.
Mr Hammond warned against the vote allowing Britain to “turn into a country that prefers to turn its back”.
“We must stay engaged with the world,” he told the BBC.
In other developments:
The BBC witnessed the aftermath of an incendiary bomb attackon a school playground in northern Syria which left scores of children with napalm-like burnsThe US said it would act in its “best interests” in dealing with the Syria crisis, following UK rejection of military interventionFrench President Francois Hollande said all options were being considered, and has not ruled out a strike within daysUN weapons inspectors visited a hospital in a government-controlled area of DamascusThe Foreign Office advised against all but essential travel to Lebanon because of a “heightened risk of anti-Western sentiment” linked to the possibility of military action in Syria. The BBC understands that the families of British diplomats are being evacuatedFormer Australian foreign minister Gareth Evans – architect of the so-called “responsibility to protect” doctrine – accused the UK of “making things up as it goes along”. He blamed the government’s “mishandling of the politics” for what he said was a “disappointing” vote against interventionThe Turkish Foreign Minister Ahmet Davutoglu said there was “no doubt” President Assad’s forces carried out the chemical attack
Labour leader Ed Miliband told the BBC: “I think ill thought-through military action would have made life worse, not better, for the Syrian people.”
He accused the government of not learning the lessons of Iraq, adding MPs had “sent a message” that British forces would not be deployed “without going through the United Nations and without ensuring we have regard to the consequences in the region”.
Earlier he said Mr Cameron was guilty of “reckless and impulsive leadership”.
And the prime minister faced criticism from his own side, with former shadow home secretary David Davis accusing him of making a “shaky argument” for intervention.
“There was feeling of rushing to action,” he told BBC Radio 4’s World at One programme. “It’s more important to get this right than to do it on a 10-day timetable”.
Former Liberal Democrat leader Lord Ashdown has been critical of the decision to not take part in military action, saying the UK was “hugely diminished”.
More than 100,000 people are estimated to have died since the conflict erupted in March 2011 and at least 1.7 million refugees displaced.
The violence began when anti-government protests during the Arab Spring uprisings were met with a brutal response by the Syrian security forces.
President Assad’s regime has blamed foreign involvement and armed gangs for the conflict.
Forces which could be used against Syria:
• Four US destroyers – USS Gravely, USS Ramage, USS Barry and USS Mahan – are in the eastern Mediterranean, equipped with cruise missiles. The missiles can also be fired from submarines, but the US Navy does not reveal their locations
• Airbases at Incirlik and Izmir in Turkey, and in Jordan, could be used to carry out strikes
• Two aircraft carriers – USS Nimitz and USS Harry S Truman are in the wider region
• French aircraft carrierCharles de Gaulle is currently in Toulon in the western Mediterranean
• French Raffale and Mirage aircraft can also operate from Al-Dhahra airbase in the UAE
See on www.bbc.co.uk