Mission unaccomplished: UK, France dispute Trump's claim of victory in Syria
Both London and Paris have also signalled they would continue working as part of the global anti-IS coalition in Syria and Iraq.
On Thursday, France's defence minister said Islamic State militants had been weakened but not wiped from the map in Syria as Trump claimed.
"Islamic State has been weakened more than ever," Florence Parly said on Twitter, responding to US President Donald Trump's announcement on Wednesday that the group had been defeated.
"But Islamic State has not been wiped from the map nor has its roots. It is necessary that the last pockets of this terrorist organisation be definitively defeated militarily."Meanwhile a UK Government spokesperson said despite "huge progress (made) since military operations began," with the coalition and its partners in Syria and Iraq recovering the vast majority of IS territory, "much remains to be done and we must not lose sight of the threat they pose".
"These developments in Syria do not signal the end of the Global Coalition or its campaign...we remain committed to the Global Coalition and the campaign to deny Daesh territory and ensure its enduring defeat," he added, using the Arabic acronym for IS.
On Wednesday, US President Donald Trump tweeted: "We have defeated ISIS in Syria, my only reason for being there during the Trump Presidency."
This was shortly followed by a surprise announcement the US is considering a full withdrawal from Syria in the coming 60 to 100 days, with State Department and other staff already being pulled out from Syria.
"The Pentagon has an order to get to move troops out of Syria as quickly as possible," a US official told the Wall Street Journal.
Around 2,000 US troops have worked alongside Syrian militant groups, most notably Kurdish forces, to defeat the Islamic State in north-eastern Syria, but pockets of fighters remain.
President Donald Trump's decision to withdraw troops from Syria has rattled Washington's Kurdish allies, who are its most reliable partner in Syria and among the most effective ground forces battling the Islamic State group.
Kurds in northern Syria said commanders and fighters met into the night, discussing their response to Wednesday's surprise announcement.
Arin Sheikmos, a Kurdish journalist and commentator, says "we have every right to be afraid."
The move is widely seen as an abandonment of a loyal ally, one that could prompt Turkey to launch a fresh offensive against the Kurds or drive the Kurds into a new alliance with Syrian President Bashar Assad, Iran and Russia.
The US move also follows a call last week between Trump and Turkish President Recep Tayyip Erdogan, who had threatened to launch an "imminent assault" on Kurdish-controlled areas of northern Syria.
Turkey views the Kurdish organisation YPG, the backbone of the US-backed Syrian Democratic Forces, as a terrorist group because of its links to the Kurdish insurgency within its territory, but the US has relied on the Kurdish forces to help defeat the Islamic State group.
Following their conversation, Erdogan said that he had received "positive answers" from President Donald Trump on the situation in north-eastern Syria.
Trump has long expressed frustration about an open-ended Syria presence, while US military and state department officials have embraced a strategy of keeping troops in the country to defeat IS and act as a deterrent to Iran's expansionist ambitions.
Officially, US forces in Syria only have authority to defeat IS and ensure the group is unable to reform.
Trump's national security adviser John Bolton said in September, however, that US forces would remain in Syria until Iran withdraws its forces.
A total withdrawal of US troops in Syria would still leave a large military presence in the region, including more than 5,000 troops in neighbouring Iraq.