At least 10 members of the Royal Sulu Army - as they call themselves - were killed in a gun battle with Malaysian police on Friday. The armed group has asked for a temporary ceasefire to bury its dead.
About 200 members of the clan landed in the coastal village of Lahad Datu in Sabah on February 9 to claim the territory as their own, citing ownership documents from the late 1800s.
President Aquino said they should leave immediately or would face prosecution at home on charges of triggering an armed conflict, but the appeals have been ignored.
In a message to the group on Saturday, Aquino said the clan members should "surrender now without conditions".
"If you have grievances, the path you chose was wrong. The just and, indeed, the only correct thing for you to do is to surrender," Aquino said.
Meanwhile, the bodies of two Malaysian police officers killed in the cross fire have been returned to their families.
Hishammuddin Hussein, the Malaysian home minister and Ismail Omar, the national police chief, were in Sabah on Saturday to oversee security operations.
Omar also urged the Filipinos to turn themselves in, saying "we have no other options but to take the necessary action to detain them".
Malaysian officials declined to say when they might move in or to elaborate on their plans.
The Filipino group is led by a brother of Sultan Jamalul Kiram III of the southern Philippine province of Sulu.
Jacel Kiram, a daughter of the sultan, indicated that her uncle, Agbimuddin Kiram, who is still in Lahad Datu, would not surrender.
"The decision remains the same -- they will not return here because honor is above life,'' she told DZBB radio in Manila. "What is life without honour?''
Abraham Idjirani, a spokesman for the sultan, said he and the council of the sultanate still had to study Aquino's statement.-Aljazeera (March 02, 2013 12:41)