incursion that had already killed 27 people and began when militants invaded to claim Malaysian territory for a past Philippine sultanate.
A day after the Philippines called for restraint, Malaysia launched the assault with fighter jets bombing the standoff village of Tanduo in Sabah state, on the northern tip of Borneo island, followed by a ground assault by troops.
"The longer this invasion lasts, it is clear to the authorities that the invaders do not intend to leave Sabah," Najib said, adding that negotiations with the estimated 100-300 intruders had gone nowhere.
"The government must take action to safeguard the dignity and sovereignty of the country as required by the people."
The Islamic intruders' apparent willingness to die over a long-dormant territorial dispute has shocked Muslim-majority Malaysia.
The group has been holed up in the village since landing by boat last month in an incursion that highlighted lax Malaysian security and the continuing threat from Islamists in the lawless southern Philippines.
At least two fighter jets were seen roaring overhead early Tuesday, followed by the thud of loud explosions, a Malaysian reporter positioned about 20 kilometres (12 miles) from the clash told AFP by phone.
"There was a series of explosions in Tanduo. Intense bombing lasted for about half an hour," followed by sporadic blasts, he said.
Amid the assault, an AFP reporter at a roadblock 30 km from Tanduo saw military transport helicopters flying toward the village, as three military trucks with dozens of soldiers and several ambulances also sped toward the scene.
National police chief Ismail Omar told reporters at a press conference hours after the operation began that security forces were still taking fire from defiant insurgents, but had launched "mopping up" operations.
Ismail said he had no firm figure on militant casualties, but added Malaysian forces were yet to suffer any in the operation, which also included police commandos.
Philippine President Benigno Aquino's spokesman blamed the intruders - followers of 74-year-old Manila-based Islamic leader Jamalul Kiram III - for the assault.
"We've done everything we could to prevent this, but in the end, Kiram's people chose this path," said the spokesman Ricky Carandang.
After a lengthy standoff, violence erupted in Tanduo on Friday with a shootout that left 12 of the gunmen and two police officers dead.
Another gun battle Saturday in the town of Semporna, hours away by road, left six police and six gunmen dead, raising fears of a wider guerrilla infiltration.
Another gunman was reportedly beaten to death by Semporna residents.
The drama may not end at Tanduo, which is set amid vast oil palm plantations.
Police said at the weekend they were hunting for a group of "foreign" gunmen in yet another town, but have provided no further updates.
Followers of Kiram, the self-proclaimed heir to the sultanate of Sulu, have said the intruders were ready to die for the cause and warned more militants were poised to land in Sabah.
Based in the southern Philippines' Sulu islands, the sultanate once controlled parts of Borneo, including Sabah.
Its power faded about a century ago but its heirs have continued to insist on ownership of resource-rich Sabah and still receive nominal Malaysian payments under a leasing deal originally struck by Western colonial powers.
The exact identities of the gunmen and their numbers have remained a mystery. Malaysia's opposition has criticised authorities for providing inadequate information on the mayhem and being caught flat-footed by the invaders.
Sabah has seen small raids by Islamic militants and criminals coming by boat from the Philippines before, but nothing on the current scale.