Sulu militants must lay down arms and surrender unconditionally and operations against them "will go on as long as it takes," Najib said at a press conference yesterday.
The 74-year-old Jamalul claims he is the head of the Islamic Sultanate of Sulu, which once controlled parts of Borneo including the site of the stand-off, as well as southern Philippine islands.
"Sabah is a part of Malaysia and in the Cobbold Commission, more than two-thirds of the people in the state voiced their intention to be part of this nation (in 1963)," Najib stressed as he had closer look at the offensive against the Sulu gunmen, which entered its third day yesterday.
Meanwhile, the fate of Sulu armed group leader Azzimudie Kiram remained unknown as Malaysian elite military and police teams entered into the final stage of search and mopping up operations at two villages today.
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Azzimudie, the brother of Jamalul, has failed to contact the Kiram family in Manila for the past two days and security forces expect to know what happened to him in a day or two.
The so-called Royal Sulu Army general identified as Haji Musa was among the some 30 gunmen killed in a shootout at Kampung Tanjung Batu on Wednesday.
The United Nations Secretary-General Ban Ki-moon has called for an end to the violence in Sabah and asked for dialogue among all the parties involved for a peaceful resolution.
Malaysian security forces on Tuesday launched an air strike using F-18 and Hawk fighter jets in the first operation to end the intrusion by Filipino gunmen who have holed up in Lahad Datu, Sabah since February 12.