Najib Razak, the Malaysian prime minister, has rejected the ceasefire offer by leader of rebels in Sabah island, saying only an unconditional surrender is acceptable.
The Malaysian prime minister, who flew to the region on Thursday to inspect security operations, said he told Philippine president Benigno Aquino by phone the ceasefire offer was rejected.
"I told President Aquino they must lay down their arms immediately," Najib told reporters in a village near where the army and police were searching for scores of rebels.
"They have to surrender their arms and they have to do it as soon as possible."
"We have given them more than three weeks to surrender and postponed it four times. We only took action after they killed eight of our policemen, so Malaysia does respect human rights," he said.
At least 31 armed Filipino gunmen have been killed in the latest offensive by the Malaysian troops. That brought the total dead close to 60, including eight Malaysian policemen.
Jamalul Kiram III, a self-proclaimed Philippine sultan, declared a unilateral ceasefire to be effective from 12:30pm local time (04:30GMT) and urged Malaysia to reciprocate, according to a statement read out by his spokesman in the Philippine capital, Manila, on Thursday.
Malaysian troops launched a major offensive against the rebels who infiltrated Sabah Island last month.
"They will not take any action. They will remain in the place where they are now. They will not expand operations," a spokesman said, referring to the rebels, believed to number between 100 and 300.
The spokesman, Abraham Idjirani, said Kiram was responding to a call by UN Secretary General Ban Ki-moon on Wednesday in which he urged an end to the violence in the Malaysian state and encourage dialogue between the opposing sides.
"The sultan is calling for a unilateral ceasefire... in order to reciprocate the call of the UN to preserve lives," said Idjirani, as the elderly and ailing Kiram sat next to him.
Anger has mounted in Malaysia over the incursion, which began on February 12 when fighters arrived from the southern Philippines province of Sulu to press Kiram's claim to the area.
At least 28 people, mostly rebels, have reported been killed as of Wednesday.
Malaysia launched an air and ground attack on Tuesday aimed at crushing the fighters who call themselves 'royal Sulu army'.
Kiram says he is the current Sultan of Sulu, although the sultanate no longer has any formal power in the Philippines.
He said his men went to Sabah to assert their claim to the area, citing ownership documents from the late 1800s.
The Sulu sultanate's power faded about a century ago but it has continued to receive nominal payments from Malaysia for Sabah under a historical lease arrangement passed down from European colonial powers.