David Cameron vowed to work with newly-reelected Barack Obama to find ways to end the bloodshed in Syria after hearing “horrendous” stories of suffering from refugees at a camp in Jordan.
The Prime Minister said his resolve to force Bashar Assad from power had been strengthened by the visit to the border region where tens of thousands of fleeing Syrians are living at the vast UN-run compound.
British humanitarian aid for the crisis would be increased by £14 million, he said, after being taken to an area of the border where up to 500 people a day are arriving.
Diplomatic talks are also planned between the UK's special envoy to the Syrian opposition Jon Wilks and rebel military chiefs in an effort to "help shape the opposition", he said.
Mr Cameron was in the country on the final leg of a three-day Middle East tour and is believed to be the first G20 leader to visit the Za'atri camp.
"I wanted to hear for myself the stories of people who have been bombed and shot and blasted out of their homes in Syria by a deeply-illegitimate and unpleasant regime that is raining down death and destruction on its own people," he said.
"It is truly horrendous to hear those stories and just redoubles my determination that now, with a newly-elected American president, we have got to do more to help this part of the world, to help Syria achieve transition."
Mr Cameron travelled by helicopter to a valley dominated by the Al Wahdah dam which is one of the busiest crossing points and was recently hit by Syrian shells.
Some of those arriving seeking shelter in Jordan had walked for up to 15 days to reach the border, he was told by the local Jordanian military chief.
At the camp, he met some of those recently arrived in the country and was treated to a patriotic Syrian song by young girls at one of the classroom tents set up for the many children living there.
Mr Cameron told them: "You are not just missed in Syria, all of the world wants to help you, including my country."
Speaking about the moves to set up talks with the rebel military leaders, he said: "There is an opportunity for Britain, for America, for Saudi Arabia, Jordan and like-minded allies to come together and try to help shape the opposition, outside Syria and inside Syria, and try to help them achieve their goal, which is our goal of a Syria without Assad."
It is a recognition that events are increasingly dictated by the military figures and not the splintered political groupings, who met in Qatar this week in an effort to forge an alliance against Assad.
And there is mounting concern that extremists are gaining a major influence inside opposition forces.
Mr Cameron left open again the possibility that the president could be allowed to flee the country voluntarily to a state where he could evade any criminal charges against him over the slaughter which has killed upwards of 30,000 people so far.
"I would like to see him face justice but, frankly, any option that involves him leaving the country and a transition taking place would be good for the people right behind me here," he said.
At present 2.5 million people inside Syria need humanitarian assistance and the number of refugees in the surrounding region is predicted to almost double to 710,000 by the end of the year.
That could mean a quarter of a million alone in Jordan.
Of the new aid, £9.5 million will go on blankets, soap and food for those forced out of their homes within Syria and on emergency help for the 8,300 Palestinian refugees based in Syria.
The rest - taking total UK aid to ease the crisis to £53.5 million - will be used to help those who have fled to Iraq, Jordan, Lebanon and Turkey - including safe transport from the border to the camps where they are being housed.
Mr Cameron will fly back to the UK after meeting with the King of Jordan for talks with German chancellor Angela Merkel but will not arrive in time for Prime Minister's questions in the Commons.
Foreign Secretary William Hague set out the details of contacts with Syrian rebel fighters in a statement to Parliament, claiming it would help the UK get a better understanding of the situation in the country.
He said the policy would build on meetings with the political representatives of the armed opposition which had begun earlier this year.
"Such groups are playing an increasingly influential role within Syria as the conflict worsens," he told MPs.
"I have therefore now authorised my officials to have direct contact with an even wider range of representatives including military figures in the armed opposition.
"This will help us to understand better the situation in Syria and the relationship between political and armed opposition groups so we can properly support political transition."
Mr Hague said all meetings with rebel military leaders would take place outside Syria and "only in environments we deem suitably secure".
He added: "Each potential contact will be explored cautiously and on a case-by-case basis.
"Through continuous assessment, we will make every effort to ensure that FCO officials engage only with legitimate representatives of the opposition."
He added: "In all contacts my officials will stress the importance of respecting human rights and international human rights norms, rejecting extremism and terrorism, and working towards peaceful political transition.
"British contacts with military elements of the Syrian armed opposition will be limited to a political dialogue including working towards an inclusive political transition."
He added that the UK would continue its policy of only supplying non-lethal support, such as radios and generators, to the unarmed opposition.