The ground troops are backed by fighter jets, with reports of several explosions near Lahad Datu, where the group of about 180 Filipinos are.
The operation to oust the clan began on Tuesday at 07:00 a.m., the Malaysian government said.
Seven army battalions were deployed to the area on Monday to reinforce police.
Among the aircraft used in the assault were an F-18 and a Hawk fighter aircraft, Malaysian state news agency Bernama reports. Helicopters were also seen flying in the area.
Malaysian National Police Chief Ismail Omar said they achieved their targets in the offensive and that there were no troop casualties.
Ismail Omar did not provide any details about the Filipinos, who he said fired at the Malaysian troops. But a spokesman for the group told Philippine television the men were safe, Reuters news agency reports.
The Filipinos landed at a coastal village in Lahad Datu district on the island of Borneo last month, saying that the territory was theirs.
Calling themselves the Royal Army of Sulu, the clan members said they were descendants of the Sultanate of Sulu in the southern Philippines, which ruled parts of northern Borneo for centuries, and demanded that the Malaysian government pay more money to lease their land.
Malaysia refused their demands and urged the group to return home.
On Monday, the Philippine government appealed to Malaysia to exercise maximum restraint and avoid further bloodshed, and sent Foreign Affairs Secretary Albert del Rosario to Kuala Lumpur for talks.
Officials said he would request that a Philippine navy ship be permitted to sail to Lahad Datu to bring the clan members home.
In the capital, Manila, protesters are outside the Malaysian embassy, urging a peaceful resolution to the stand-off, reports say.
“We’ve done everything we could to prevent this, but in the end, Kiram’s people chose this path,” Philippine presidential spokesman Ricky Carandang said on Tuesday of clan leader Jamalul Kiram III.
Eight Malaysian troops and 19 clan members have already been killed in the three-week stand-off.
Twelve were killed along with two Malaysian policemen when Malaysian security forces tried to tighten the cordon around the occupied village on Friday.
The incident sparked violence in another area over the weekend, in which seven clan members and six policemen died.
Jamalul Kiram’s brother has said they are not violating any laws because Sabah is “owned by the Sultan of Sulu” and insisted that they have a right to defend themselves if attacked.
However, Malaysian Prime Minister Najib Razak said over the weekend that its forces were authorized to “take any action deemed necessary”.
In a statement on Tuesday, Najib Razak said the assault had become necessary because security forces had been killed and Malaysians in Sabah feared for their safety.
“After the first attack, I stressed that the intruders must surrender themselves or the security forces will have to act,” he said in comments carried by Bernama.
Najib Razak said police had held negotiations with the Filipinos in the hope they would leave peacefully, but that “as the intrusion prolonged it was evident to the authorities that the intruders had no intention of withdrawing from Sabah”.
“The government has to take the right action in order to preserve the pride and sovereignty of this country,” he said in his statement.
Najib Razak has come under increasing political pressure in Malaysia to end the incursion, with the opposition criticizing him for allowing it to continue. The Philippine government is also coming under pressure to do more to protect the Filipino clan.
Sabah shares a sea border with the southern Philippines, which is home to a number of Islamic militant and kidnap-for-ransom groups. The journey between the two can take only a few hours.
It formed part of the Sulu Sultanate – which once spread over several southern Philippine islands as well as parts of Borneo – before it was designated a British protectorate in the 1800s.
Sabah became part of Malaysia in 1963, and the country still pays a token rent to the Sulu Sultanate each year.
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