Malaysia has rejected a call for a ceasefire by a Philippine Muslim clan who launched an incursion into a village in Sabah last month, saying the land belongs to them.
PM Najib Razak said they want the group "to unconditionally surrender".
The ceasefire offer by the group's leader based in Manila came after UN Secretary General Ban Ki-moon called for an end to the violence in Sabah.
Since fighting began, 60 people have died: 52 Filipinos and eight policemen.
Malaysian National Police Chief Ismail Omar was quoted as saying that at least 31 Filipinos have been killed this week.
"We want the militants to unconditionally surrender and hand over their weapons," Mr Razak told media during his first trip to the area since violence broke out.
He added that the military would continue to track them down "for as long as it takes to eliminate them" if they did not surrender.
In a statement released earlier, Mr Ban's office said he encouraged all sides to engage in dialogue to resolve the situation peacefully.
"The Secretary-General expresses concern about the impact this situation may have on the civilian population, including migrants in the region," said the statement.
"He urges all parties to facilitate delivery of humanitarian assistance and act in full respect of international human rights norms and standards."
The Manila-based leader of the Filipino clan, Jamalul Kiram III - one of several men who claims the title of Sultan of Sulu - said earlier this week they they were prepared to "fight to the last man".
But on Thursday, Mr Kiram issued a statement following Mr Ban's comments and called for a ceasefire to the violence in Sabah at 12:30 local time (04:30 GMT).
"They will not take any action. They will remain in the place where they are now. They will not expand operations," his spokesman, Abraham Idjirani, told reporters in Manila.
"We hope Malaysia reciprocates the same call for a ceasefire," he added.
The group of some 200 Filipinos landed at a coastal village in the Lahad Datu district of Sabah, on Malaysian Borneo, saying that the territory was theirs.
Calling themselves the Royal Army of Sulu, the clan members said they were descendants of the Sultanate of Sulu in the southern Philippines, which ruled parts of northern Borneo for centuries, and demanded that the Malaysian government pay more money to lease their land.
Initial attempts by both the Philippines and Malaysian government to persuade them to leave failed, and late last week, clashes broke out between the clan and Malaysian police, leaving eight policemen and 19 clansmen dead.
On Tuesday Malaysian troops backed by fighter jets raided the area around Tanduo, where the clan were holed up. On Wednesday they then carried out extensive searches of the area, saying some of the Filipinos could be hiding among the local population.
The clan said on Wednesday that none of its members had been killed, but later in the day, Malaysian officials displayed what they said were photographs of 13 bodies they had found in a shallow grave in Tanduo.
It was not clear whether they had died during the assault or in last week's clashes.
Both the Malaysian and Philippines governments are coming under increasing public pressure to end the ongoing crisis.
A rally was held in the Philippines capital, Manila, on Wednesday night calling for a peaceful resolution and expressing concern for the safety of the many Filipinos who live and work in Sabah.