President Donald Trump has warned Syria's government the US is "locked and loaded" to strike again if it carries out chemical attacks.
The warning came after the US, UK and France struck three Syrian sites in response to a suspected deadly chemical attack in the town of Douma a week ago.
Syria denies any chemical use and says that attack was fabricated by rebels.
A UN Security Council vote brought by Syria's ally, Russia, to condemn the US-led strikes was rejected.
The wave of strikes represents the most significant attack against President Bashar al-Assad's government by Western powers in seven years of Syria's civil war.
While Western powers have supported rebels from early on in the war, they have not intervened against Syria directly.
After the failure of the Russian motion, the US, UK and France circulated a new draft resolution to UN Security Council members, calling for an independent investigation into Syria's alleged use of chemical weapons, AFP news agency reported.
A similar previous plan had been vetoed by Russia.
UK Prime Minister Theresa May has blamed Russian obstruction for the need to launch military strikes, saying they left "no practicable alternative".
Inspectors from the independent Organisation for the Prohibition of Chemical Weapons (OPCW) had already been dispatched to Damascus and they are expected to visit Douma this weekend.
But the OPCW will not seek to establish - and publicly announce - who was responsible for the attack, which is what the UK, US and France want to see.
The new, Western-drafted resolution calls for the OPCW to release their report within 30 days.
UK foreign secretary Boris Johnson wrote in the Telegraph that global powers will not "turn a blind eye" to the use of chemical weapons.
Syria's Assistant Foreign Minister Ayman Sousan told the BBC his government welcomed the OPCW delegation.
"The work of the mission is in the interest of the Syrian state as it will uncover the lies, hypocrisy and the misinformation of the sides which had promoted the alleged use of chemical weapons," he said.
