Today's clashes saw the highest number of casualties in a single day, which has left 60 people dead since nearly 200 members of a Filipino Muslim clan took over an entire village last month, police said.
Less than two hours before the announcement of the casualties, Malaysian Prime Minister Najib Tun Razak said Sulu militants must lay down arms and surrender unconditionally and operations against them "will go on as long as it takes", rejecting the cease-fire call.
"Do not underestimate Malaysia's determination to maintain Sabah as part of Malaysia," he said.
Malaysia's Defense Minister Ahmad Zahid Hamidi earlier tweeted "do not trust the ceasefire offer by Sultan Jamalul Kiram. In the interests of the people of Sabah and Malaysia, destroy all the militants."
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Police and military forces tracking Filipino intruders have waged a fierce gunbattle that resulted in the deaths of 31 clansmen today, national police chief Ismail Omar said, adding that no Malaysians were injured.
"We have created a tight cordon around the area, with the help of the Navy at sea and Armed Forces on land. Their food supplies are cut off because we have caught many of the intruders during their attempts to get food," said Sabah Police Commissioner Hamza Taib to a tv channel.
The self-proclaimed Sulu sultan Sultan Jamalul Kiram had called for an immediate ceasefire following calls by United Nations Secretary General Ban Ki-moon to end violence in Sabah and start holding dialogues.