Thailand, however, says it has photographs showing dissidents responsible for various acts of violence being trained in hideouts in Malaysia.
Najib urged Bangkok to hand over the evidence it had.
"Our stand is that we have no information as alleged by them," Najib told a news conference. "There is no camp in the northern part of the peninsula."
Thai Prime Minister Thaksin Shinawatra upset Malaysia and Indonesia by saying Thai dissidents had trained in the jungles along the border with Malaysia, and had been exposed to radical ideas in Indonesia, where members of Jemaah Islamiya are alleged to have launched attacks.
Thaksin said the Malaysian and Indonesian governments had never supported the groups and were cooperating with Bangkok, but his weekend remarks angered them, drawing a response from Malaysian Prime Minister Abd Allah Ahmad Badawi, who asked for evidence to support the claims.
"If the Thai government has information, it is better for them to inform the Malaysian government through official channels in confidence," Najib said, speaking after a weekly cabinet meeting.
"To us, this is outside the international norms because this involves sensitive information. Sensitive information should be handled appropriately."
Malaysia says there is no training
going on in its territory
But Malaysia has no plans to respond with an official protest, or by closing the border with Thailand, Najib added.
"We want good ties with Thailand to continue. We hope they handle this case with care," he said. "It is incumbent upon them to give us the information rather than for us to go to them.
"The ball is in their court."
Najib said he did not know how Thai authorities obtained the pictures of training camps that Thai Deputy Interior Minister Sutham Saengprathum referred to on Tuesday.
Sutham did not show reporters the pictures or describe them, but he said they proved that training camps existed in Malaysia's northern Kelantan province.
Later, he said the pictures had been taken by Thai agents this year, with the help of Malaysian intelligence.
"According to our knowledge, there are about 10 ringleaders in Kelantan state," he said.
Bangkok has alleged several times over the past 11 months that dissidents flee to Malaysia after carrying out attacks.