The Prime Minister made the comments during a telephone call with the Turkish president (Picture: PA).
Boris Johnson has expressed his "grave concern" over the situation in Syria and has urged Turkey to halt its offensive on the north-east of the country.
In a telephone call with President Recep Tayyip Erdogan, the Prime Minister said the assault could worsen the region's humanitarian crisis and "undermine" the fight against so-called Islamic State (IS).
According to a Number 10 spokesman, Mr Johnson said although Turkey is an "important partner", the UK "cannot support" its military action in Syria.
"He [Mr Johnson] urged the president to end the operation and enter into dialogue, and said the UK and international partners stand ready to support negotiations towards a ceasefire," the spokesman said.
The incursion against the Syrian Kurds - who played a key role in defeating IS' self-proclaimed Caliphate alongside nations including the US and UK - has been widely criticised by western countries.
Turkey, which views the Kurdish-led forces in the region as terrorists, says it wants to create a 20-mile "safe zone" along its border with Syria.
The United Nations says more than 100,000 people in north-east Syria have fled their homes since the assault began on Wednesday.
There are also concerns that hundreds of suspected IS prisoners, currently guarded by Kurdish forces, may escape during the chaos.
Mr Johnson's comments come after Foreign Secretary Dominic Raab called on Turkey to show "maximum restraint", admitting he fears the humanitarian situation "could be made worse".
Turkey launched its offensive just two days after the withdrawal of US troops from the area.
US President Donald Trump said he wanted to stop getting involved with "endless wars".
The decision has been heavily criticised with Mr Trump being accused of endangering regional stability and risking the lives of Syrian-Kurdish allies.