(CNN) -- Malaysian fighter jets and soldiers on Tuesday waged an offensive against a group of armed invaders from the Philippines, who have staked a claim to a remote part of the island of Borneo, authorities said. Previous efforts by Malaysian police to turn the men back had ended in deadly clashes.

The group of Filipino men, believed to number between 100 and 300, arrived three weeks ago on the east coast of the Malaysian state of Sabah, on Borneo, demanding to be recognized as representatives of a sultanate that used to rule the area.

Malaysian authorities initially tried to persuade the men to return peacefully to their homes in the nearby southern Philippines. But the intruders refused to budge, and the standoff turned violent in recent days as clashes in the region reportedly left nine Malaysian police officers and 19 intruders dead.

"Our security forces were attacked and killed. Malaysians, particularly those in Sabah, are worried about their safety," Malaysian Prime Minister Najib Razak said in a statement carried by the national news agency Bernama announcing the offensive Tuesday.

The standoff has touched on an unresolved territorial issue between the Philippines and Malaysia, as well as Manila's efforts to improve relations with Islamic insurgents in the country's south after decades of violence.

The Malaysian operation Tuesday morning in Lahad Datu, the district in Sabah where the Filipino men had come ashore, involved an air raid by F-18 and Hawk fighter jets followed by mortar fire and a ground assault by soldiers, Bernama reported.

The security forces "achieved their objective," the news agency cited Tan Sri Ismail Omar, the head of the Malaysian Police, as saying without elaborating on what exactly the goal had been.

No members of the Malaysian forces were hurt in the attack, and the casualties on the Filipino side had yet to be determined, he said.

But representatives of the Filipino group didn't report any initial losses from the offensive, saying the Malaysian jets had dropped bombs at a location they had occupied previously.

Filipino group on Borneo claims to represent sultanate, Malaysia says

'The Royal Army'

The Filipino men have called themselves the Royal Army of the Sultanate of Sulu, a former Islamic power in the region that once controlled parts of the Philippines and Borneo. Its influence has since faded, and it is now a clan in the poor, restive southern Philippines.

The sultanate's leadership has been riven by internal power struggles in recent decades, but the squabbling family members appear to have united in the decision to send their followers to Sabah, a move that has alarmed Malaysians and complicated efforts by the Philippines to pursue peace talks with Muslim rebels in its southern islands.

Abraham Idjirani, a spokesman for one of the sultanate's leaders in Manila, said the armed the Filipino men reported hearing shots being fired nearby, but had so far suffered no casualties.

Idjirani blamed Malaysian authorities for the escalation of the standoff, saying they had fired the first shots in the clash that took place between the two sides on Friday. He added that a woman and family members of Sabah residents had been killed in that skirmish.

He also claimed that other people in the region were joining the sultanate's followers in the fight against the Malaysian forces but was unable to provide details.

"We don't know who they are, but they are there," he said.

Since the crisis began, Philippine authorities have urged the sultanate's followers to lay down their arms and return home.

"From the very start, our objective has been to avoid the loss of lives and the shedding of blood," President Benigno Aquino III said at the weekend. "If you have grievances, the path you chose was wrong. The just, and indeed, the only correct thing for you to do is to surrender."

Excluded from a peace deal

The Sabah standoff has its roots in a recent landmark peace deal between Manila and Muslim rebels, according to Julkipli Wadi, the dean of the Institute of Islamic Studies at the University of the Philippines.

The members of the sultanate's royal family seem to have felt isolated by the provisional accord signed in October by the Philippine government and the Moro Islamic Liberation Front, which has fought for decades to establish an independent Islamic state in southern Philippines, Wadi said last month.

The sultanate has succeeded in grabbing the attention of Philippine and Malaysian authorities. But the resulting violence makes the outcome of the situation unclear.

Established in the 15th century, the Sultanate of Sulu became an Islamic power center in Southeast Asia that at one point ruled Sabah.

But the encroachment of Western colonial powers, followed by the emergence of the Philippines and Malaysia as independent nation states, steadily eroded the sultanate's power, according to Wadi.

It became "a sultanate without a kingdom" to rule over, he said. Sulu is now a province within the Republic of the Philippines.

The economic, cultural and historical links between Sabah and the nearby Philippines islands, as well as the porous nature of the border between the two, means that many of the sultanate's followers have friends and relatives in Lahad Datu.

And the historical connection still fuels tensions between Malaysia and the Philippines, with Manila retaining a "dormant claim" to Sabah through the Sultanate of Sulu, according to the CIA World Factbook.

The Philippines claims much of the eastern part of Sabah, which was leased to the British North Borneo Company in 1878 by the Sultanate of Sulu. In 1963, Britain transferred Sabah to Malaysia, a move that the sultanate claimed was a breach of the 1878 deal.

Malaysia still pays a token rent to the sultanate for the lease of Sabah.

CNN's Kathy Quiano contributed to this report.