The three powers also agreed at talks in Paris that Assad would face "serious consequences" if he fails to comply with a UN resolution setting out a timetable for the handover of Syria's chemical weapons to international control, French Foreign Minister Laurent Fabius said.
US Secretary of State John Kerry did not use the word "serious", saying: "If Assad fails to comply with the framework we are all agreed that there will be consequences."
Kerry, who agreed the terms of the weapons handover with his Russian counterpart in Geneva on Saturday, said the allies were committed to keeping up the pressure on Assad.
"Each of us here today are here to emphasise the same thing, that what we achieved in this agreement has to be translated into a UN resolution, it has to be strong, it has to forceful it has to be real, it has to be transparent, it has to be timely, all of those things are critical, and it has to be enforced. If the Assad regime believes that this is not enforceable and we are not serious, they will play games."
Fabius announced there would be a major international meeting with leaders of the Syrian National Coalition on the sidelines of the UN General Assembly in New York next week.
"We know that in order to negotiate a political solution, there has to be a strong opposition," Fabius said.
French officials said Russia had been invited to the conference.
Kerry also stressed that the allies were "committed to the opposition" and said Assad had "lost all legitimacy to be possible to govern his country."
The signal of support for the rebels came in reaction to criticism of the chemical weapons deal from opposition leaders, who fear it could consolidate Assad's grip on power.
France, UK and US will submit a draft resolution on Syria to the UN Security Council within few days or hours together with other countries stated French Foreign Minister Laurent Fabius on Monday.
The US, UK and France have also agreed to bolster Syrian rebels by providing more help, French Foreign Minister Laurent Fabius announced at a joint media conference with his counterparts from Washington and London.
"If (Syrian leader Bashar al-) Assad fails in time to abide by the terms of this framework, make no mistake, we are all agreed - and that includes Russia - that there will be consequences," Kerry said at a news conference in Paris with his French and British counterparts.
The resolution should employ the "strongest, most forceful terms possible" to ensure compliance by the Syrian regime, US Secretary of State John Kerry added.
French Foreign Minister Laurent Fabius warned of "serious consequences" if the Syrian regime dodged its commitments.
On Sunday, President Hollande said "the military option must remain" to force Syria to give up its chemical arsenal.
Earlier last week US and Russian officials reached an ambitious agreement calling for an inventory of Syria's chemical weapons programme within a week, with the programme eradicated by mid-2014.
A UN resolution would detail how Syria can secure and destroy its stockpile. The content of that is under discussion on Monday.
The UN's chief weapons inspector submitted his team's report on the August attack on Sunday.
The August 21 attack unfolded as a UN chemical weapons team was in Syria to investigate earlier reported attacks.
After days of delays, the inspectors were allowed access to victims, doctors and others in the Damascus suburbs afflicted by the poison gas.
The UN's chief weapons inspector turned over his team's report on Sunday, and the Security Council is due to take it up in a closed session on Monday.
United Nations chief Ban Ki-Moon has received the report from experts on chemical weapons in Syria and will submit it to the UN Security Council on Monday morning, according to the press service of the world organization.
"The report by the UN mission to investigate allegations of the use of chemical weapons in the Syrian Arab Republic has been submitted to the Secretary General,"- said the statement.
On Monday morning, September 16, Ban Ki-Moon "will inform the UN Security Council on the report during closed consultations."
Ban Ki-Moon will present the report to the UN Security Council at 11:15am (1515 GMT). He has already revealed that he expects the report to give "overwhelming" confirmation that chemical weapons were used in an attack near Damascus on August 21 in which hundreds died.
The UN team, however, is not allowed to say who carried out the attack.
Damascus will commit to a US-Russian plan to eradicate its chemical weapons once it has United Nations approval, Syria's information minister told British television Sunday, adding that the regime had already begun preparing relevant documents.
"Syria is committing itself to whatever comes from the UN," Omran al-Zoubi told ITN. "We accept the Russian plan to get rid of our chemical weapons. In fact we've started preparing our list.
"We are already documenting our papers and we have started to do our job," he added. "We don't waste time."His comments come a day after US Secretary of State John Kerry and his Russian counterpart Sergei Lavrov announced an ambitious deal to dismantle and destroy Syria's chemical arms stockpile by mid-2014.
Syria will implement the US-Russian deal when it "turns into something more concrete" following a UN Security Council vote, Zoubi said.
"For 40 years Syria has always been trusted once it has committed itself."
Zoubi vowed that war-torn Syria would "absolutely" grant access to weapons inspectors, saying the country "respects and honours what it says."
"We take this agreement very seriously," the minister said.
The threat of US military action against Syria remains "real", Washington's top diplomat said on Sunday a day after striking a deal with Russia to destroy Damascus's chemical weapons stockpile.
"The threat of force remains, the threat is real," US Secretary of State John Kerry said at a news conference in Jerusalem with Israeli Prime Minister Benjamin Netanyahu.
"Now this will only be as effective as its implementation will be and (US) President (Barack) Obama has made it clear that to accomplish that, the threat of military force remains," he said.
"We cannot have hollow words," he warned, because that would affect other players affecting the international community, including Iran and North Korea.
Kerry's remarks were made following a four-hour meeting with Netanyahu at which the two men discussed the US-Russian agreement on eradicating Syria's stockpile of chemical weapons, and also talked about the ongoing Middle East peace talks.
"Make no mistake, we have taken no options off the table," Kerry warned after news of the deal appeared to stave off the threat of a US-led military strike on the Syrian regime after a chemical attack last month on a Damascus suburb.
"The fact of weapons of mass destruction having being used against the people of their own state - these are crimes against humanity and they cannot be tolerated," he said.
Standing next to him, Netanyahu said stripping Syria of its chemical stockpile would make the entire region "a lot safer".
"The world needs to ensure that radical regimes don't have weapons of mass destruction because, as we've learned once again in Syria, if rogue regimes have weapons of mass destruction they will use them," he said.
"If diplomacy has any chance to work it must be coupled with a credible military threat," Netanyahu said.