The Comoran invasion force was supported by African Union troops
Troop invasion
They said troops backed by an African Union force had taken Anjouan's main city and airport with light resistance.
But fighting continues in some areas and the whereabouts of rebel leader Col Mohammed Bacar is unclear.
His re-election as president of the semi-autonomous island of Anjouan last year had been declared illegal.
Surrender call
Defence Minister Bacar Dossar said coalition forces had not yet secured total control of the island and were "trying to flush out a pocket near [Col Bacar's] residence in Barakani".
There were other small areas of resistance, he told the BBC, adding that so far neither the AU troops nor the Comoros army had suffered any casualties.
Officials said government forces had arrested several high-ranking aides of Col Bacar, but were still looking for the rebel leader himself.
About 450 Comoran and AU troops landed in a seaborne assault at dawn on Tuesday. Mortar and machine-gun fire was heard.
The invading force captured the airport at Ouani and the main city, Mutsamudu. The presidential palace was abandoned.
The Comoran troops are being supported by a nearly 1,500-strong AU force, including Tanzanian and Sudanese soldiers.
I have ordered the Comoran army and the forces of our country's friends to bring Anjouan back under the rule of law and free her citizens
Ahmed Mohamed Sambi
Comoros President
In pictures: Comoros assault Q&A;: Comoros rebellion
As the assault was launched on Monday night, Comoran President Ahmed Mohamed Sambi said: "I have ordered the Comoran army and the forces of our country's friends to bring Anjouan back under the rule of law and free her citizens."
Residents of the island were pictured greeting the government forces with jubilation as they patrolled through the streets, with some of the crowds chanting "Bacar is a dog".
Fractious history
Five boats carrying the Comoran and AU troops had left the island of Moheli overnight on Sunday, while a helicopter dropped leaflets over Anjouan warning citizens that the assault to retake the island would begin in hours.
The Comoros archipelago has had a fractious history since independence from France in 1975, experiencing more than 20 coups or attempted coups.
The three main islands of the archipelago lie 300km (186 miles) off Africa's east coast north of Madagascar.
Mr Bacar was elected president of semi-autonomous Anjouan in 2002. His re-election in 2007 was declared illegal by the federal authorities on Grand Comore who declared Anjouan to be in rebellion.
The AU condemned Mr Bacar's move and agreed to provide troops to topple him.
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Location of ComorosComoros, backed by African Union forces, has invaded the island of Anjouan in an effort to topple the rebel leadership of Mohamed Bacar, who has been seeking independence from Comoros.

Around 450 troops disembarked on Monday, landing in the capital of Mutsamudu on Tuesday at dawn, where a jubilant crowd cheered for them. They joined the nearly 1,500 African Union forces from Sudan and Tanzania, with Libya, France, and the United States providing logistical support for the operation.

The Comoros government says they have already captured most of the island. "The operation started in the early morning hours and it is going smoothly and according to plan," said Abdourahim Said Bakar, a government spokesman. "The military has taken control over most of the island - the airport and Anjouan's capital, Mutsamudu." 

There have been no official reports of casualties, but two African Union soldiers appear to have suffered minor injuries, and one reporter saw an elderly man being carried away after apparently being hit by a stray bullet. Sounds of machine guns and heavy artillery could be heard throughout the island.

Mohamed Bacar seized control of Anjouan in a 2001 military coup. After his term expired in 2007, he held his own elections in which he declared himself the winner. This election was viewed as illegal by Comoros and the African Union.

"We hope that by the end of the day we will have the problem resolved," the government spokesman said. "A special group has been selected to capture Bacar, arrest him and bring him to court. He has to pay for his crimes." 

The spokesman also outlined his priorities for Anjouan once the island is stabilized, which included holding elections within three months, disarming Bacar's miltias, and putting Bacar on trial for corruption and human rights abuses once he is found.

The troops met some resistance from supporters of Mohamed Bacar, armed with assault rifles and rocket launchers and numbering around 400. Some loyalists gathered near Bacar's residence in Barakani, but the military soon took control of the area. The residence was searched, but Bacar was nowhere to be found.

The Bacar loyalists have reportedly begun using guerrilla tactics against the invading forces. "I have over a hundred men and we will fight until we die," said Lieutenant Ibrahim Moussa of the loyalists. "It's God's will that will decide who is to win and who is to die. The invaders won't make it through."

Though one Comoros soldier reports that three of Bacar's highest-ranking supporters have been arrested, Bacar himself remains at large. The government spokesman says he has been seen fleeing to the island of Mayotte by canoe. 

"Colonel Mohamed Bacar has been spotted in the village of Sadanpoini where he is heading without doubt for a place to flee on board a kwassa (small canoe) towards Mayotte Island," Abdourahim Said Bacar said. "It seems, according to various sources, that he is dressed as a woman," he added.

However, this information has not been confirmed. "The Comoran command will not confirm any information regarding the arrest of Colonel Bacar," said reporter Franck Berruyer.
 
In a nationally televised address, Comoros president Ahmed Abdallah Mohamed Sambi said he had approved of the military operation. "I have ordered the Comoran army and the forces of our country's friends to bring Anjouan back under the rule of law and free her citizens," he said.

Meanwhile, South African president Thabo Mbeki denounced the operation. "It takes Comoros back to the use of force to solve a problem that could have been resolved with negotiations," he said in a televised statement. "There was no need to deploy troops."