Macron and May both suggested on Thursday that enough evidence had been gathered to pin blame for the attack on Assad.
"It sounds like all options are on the table, and a final decision hasn't been made, but we'll keep you posted once it is", White House Press Secretary Sarah Sanders told reporters at her daily news conference.
The Kremlin spokesman is warning the USA and its allies against any steps that could destabilize the situation in Syria.
Asked to comment on possible US strikes, President Vladimir Putin's spokesman said Thursday that "it's necessary to avoid any steps that may fuel tensions in Syria". He added that it would have an "utterly destructive impact on the Syrian settlement".
The President also insisted that the U.S. would not remain engaged in Syria forever under any circumstances.
But since then he's suggested he'll wait for further advice from military advisers and U.S. allies.
China called on all parties to the issue to ease the tension as soon as possible, Geng said.
Trump had vowed to take swift and decisive action against Syria since reports of a suspected poison gas attack on a rebel enclave that killed dozens of people.
He criticized Russia's support of the Syrian regime saying "Russia must decide if it will continue down this dark path".
The Syrian government and Russian Federation, which backs it, strongly oppose the claims, which they say are fabricated.
Senator Edward Markey, a member of the Senate Foreign Relations Committee, criticised Trump's warnings that he intends to conduct military strikes in retaliation against Assad's use of chemical weapons.
"We'll be coming out of Syria, like, very soon", he said.
A United Kingdom -based Syrian monitor says that troops have been emptying airports and bases, while opposition fighters have told Sky News Arabia that government-allied forces have been retreating from some positions and moving equipment.
Syria 'Chemical Attack': US Weighs Up Military Response
The same officials say Syria has continued to produce or procure chlorine, which also has industrial and agricultural uses. Russian military police have started patrolling the site of last weekend's alleged chemical attack in Syria .
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Assad was quoted by state television on Thursday as saying that the government's battlefield victories led Western states to raise their voices, but any action they took would only destabilise the region.
"Syria's enemies are angry because of its military advances against terrorist groups", Ali Akbar Velayati, Supreme Leader Ali Khamenei's top adviser, told Iranian state TV during his visit to eastern Ghouta's bomb-shattered ruins.
A day earlier, European airspace authorities warned aircraft to be careful over the next few days when flying close to Syria because of the possibility of air or missile strikes into the country.
Formally, the prime minister has the right to go to war without approval from parliament, but a convention has been established in previous conflicts where MPs have a vote either before or shortly after military action begins. That meant airstrikes, possibly in tandem with France and other allies that have expressed outrage at the alleged Syrian chemical attack, could be launched within hours of a presidential decision.
May and Trump had also "agreed it was vital that the use of chemical weapons did not go unchallenged, and on the need to deter the further use of chemical weapons by the Assad regime".
Half a world away in New York, Russia's United Nations ambassador warned the priority in Syria was to avert US-led strikes that could lead to a unsafe confrontation between the world's two preeminent nuclear powers.
Parliament voted down British military action against Assad's government in 2013, in an embarrassment for May's predecessor, David Cameron.
Similarly, French President Emmanuel Macron said he had "proof" that the Syrian government had attacked Douma with chemical weapons, without giving further details.
The OPCW, which works to rid the world of chemical arms stockpiles, said its experts were on their way to Syria and will start their work on Saturday.
Asked about consulting the U.S, which has also threatened military action, Le Drian said "France is autonomous in taking its decisions".
President Donald Trump huddled with top national security advisors Thursday to weigh his military options in Syria, as Moscow warned against any move that risks triggering a conflict between Russian Federation and the United States. Syria has denied carrying out such an attack.
In Syria, there are reports that forces allied with the Syrian government have been relocating from various military sites and bases in anticipation of a possible attack.