Turkey's President Recep Tayyip Erdogan said that Syrian government forces in Idlib must pull back behind a line of Turkish observation posts by the end of this month or his forces will drive them back
The regime's offensive has caused one of the biggest waves of displacement in the nine-year war.
Tensions have increased between Ankara and Damascus after a deadly exchange of fire.
Speaking two days after eight Turkish military personnel were killed by shelling in Idlib, prompting Turkey troops to kill 13 Syrian government soldiers in retaliation, Mr Erdogan said two Turkish posts were now behind the Syrian government front line.
" If the regime does not pull back, Turkey will be obliged to take matters into its own hands," he said.
Turkey killed at least 13 Syrian government troops in response, according to monitors, in the deadliest clashes since Ankara sent troops to Syria in 2016.
Weeks of intensive aerial bombardment and a bruising ground offensive have emptied entire towns in the north-west province and forced civilians to flee north towards the Turkish border.
"Since December 1, some 520,000 people have been displaced from their homes, the vast majority – 80 per cent – of them women and children," said David Swanson, spokesman for the United Nation's Office for the Co-ordination of Humanitarian Affairs.
The exodus, coinciding with a biting winter, is one of the largest since the 2011 start of a conflict that has displaced more than half of Syria's pre-war population of 20 million.
"This latest displacement compounds an already dire humanitarian situation on the ground," Mr Swanson said.
The UN was alarmed by the plight of more than three million people – half of them displaced by violence elsewhere – who live in Idlib province and surrounding areas, he said.
UN Secretary General Antonio Guterres called the escalation "extremely worrying".
But US Secretary of State Mike Pompeo backed Washington's Nato ally, calling the Syrian mortar attack "a grave escalation" and said US officials "fully support Turkey's justified self-defence actions in response".
Syrian forces have retaken dozens of villages and some major towns – including the former rebel bastion of Maaret Al Numan – and continue to advance, pushing displaced populations ever closer to the Turkish frontier.
Mr Erdogan accused Damascus of driving "innocent and grieving people in Idlib towards our borders".
Turkey, which already hosts more than three million displaced Syrians, is keen to stop another mass influx.
Mr Erdogan criticised Russia, a key backer of President Bashar Al Assad's regime, for failing to enforce peace agreements in the region and urged Moscow to "better understand our sensitivities in Syria".
He said this week's clashes amounted to a "new era" in Syria, and that any further attacks would be "responded to in kind".
"The air and ground elements of the Turkish armed forces will freely move in the Idlib region and if needed will launch an operation," he said.
"From now we will not turn a blind eye to any step that constitutes the violation of the agreements."
As part of a 2018 deal with Moscow, Turkey set up 12 observation posts in Idlib, one of which was surrounded by Mr Al Assad's forces in December.
Russia agreed to prevent Damascus from launching a devastating operation in the densely populated region.
Turkey was to contain the extremist groups running the region, but instead, the forces it supports have been sidelined by Syria's former Al Qaeda affiliate, Hayat Tahrir Al Sham, which dominates Idlib.