By Angie Teo

FELDA SAHABAT, Malaysia (Reuters) - Malaysian security forces said they killed 31 Filipino militants in overnight clashes in eastern Sabah state as Prime Minister Najib Razak rejected a ceasefire offer from the armed group staking an ancient claim to the resource-rich region.

At least 52 militants and eight Malaysian policeman have died in clashes that began in the northern tip of Borneo island last Friday and intensified into an all-out assault by army troops early this week.

Security officials said many militants escaped the military attacks aimed at a coastal village where they had been holed up for weeks. The obscure group is believed to be at large in surrounding oil palm estates.

"We want the militants to unconditionally surrender and hand over their weapons," Najib said in his first trip to the conflict area since the standoff began a month ago.

If they did not surrender, Najib said the military would continue to track them down "for as long as it takes to eliminate them."

Malaysia's police chief, Ismail Omar, addressing a separate news conference, announced the toll of 31 militants killed in the latest clashes.

"We've narrowed it to two village areas," Omar told reporters, referring to two settlements close to the site of the initial military attack.

The month-old confrontation in Sabah was sparked when the armed group numbering about 200 arrived from the nearby southern Philippines to press an old claim to the resource-rich region.

The conflict has strained relations between the Southeast Asian neighbors and prompted speculation that Najib may delay a national election he had been expected to call as early as March and which must be held by June.

The group is demanding recognition and an increased payment from Malaysia for their claim as the rightful owners of Sabah, part of Borneo island leased by the sultanate to British colonialists in the 19th century.

Malaysia has refused the demands and Manila has repeatedly told the group to put down its weapons and come home.

Najib said he had conveyed Malaysia's position to Philippine President Benigno Aquino by telephone. Aquino has said he suspects his country's opposition backed the group in an attempt to undermine him ahead of congressional elections in May.

The self-proclaimed Sultan of Sulu, Jamalul Kiram III, offered a unilateral ceasefire earlier in the day.

"We hope Malaysia will reciprocate this gesture," Abraham Idjirani, the sultan's spokesman, said in Manila.

U.N. Secretary-General Ban Ki-Moon called for an end to the violence and talks for a peaceful resolution.

(Reporting by Angie Teo and Manny Mogato in Manila; Writing by Siva Sithraputhran; Editing by Stuart Grudgings and Ron Popeski)