Fighting broke out on Wednesday when police loyal to Bacar attacked soldiers who had taken over official buildings in order to install an interim leader.
Jose Francisco Madeira, a special envoy for the AU, was received by the federal president, Ahmed Abdallah Sambi, who also comes from Anjouan, in the capital Moroni, and is expected to visit Anjouan on Sunday.
The AU has condemned the Anjouan police for "seriously threatening the unity and national sovereignty of the Comoros".
The Union of Comoros gained independence from France in 1975 and comprises the islands of Grand Comore, Moheli and Anjouan.
Situated in the Indian Ocean off the coast of Mozambique, the archipelago has had numerous coups and much civil strife, and in 1997 the islands of Moheli and Anjouan declared independence.
A 2001 constitution accorded each island greater autonomy including the right to its own president and constitution with the central government remaining in the Grand Comore capital, Moroni.
Comoros is a member of the AU and of the Arab League. Its population of 812,000 is almost entirely Sunni Muslim with a small Christian minority.
It is one of the poorest countries in Africa and heavily reliant on international aid.
Speaking to reporters on Saturday, the interim head of the national army, Lieutenant-Colonel Salimo Mohamed Amiri, said Bacar's men had "seized the moment to carry out a long-prepared offensive".
His predecessor was sacked over mismanagement of the Anjouan crisis.
Amiri said that on Wednesday, about 75 army soldiers based in Anjouan had fought 1,200 men loyal to Bacar. They held them off for two hours, but were bombarded when they tried to leave the island by speedboat.
Anjouan was said to be calm on Friday and Saturday.
However, witnesses said central government troops had moved into nearby Moheli island on Saturday.
The power struggle on Anjouan has highlighted deep rivalries on the Indian Ocean archipelago, whose three main islands share a rotating national presidency but retain autonomy through local leadership under the terms of a 2001 peace deal.
The islands have seen 19 successful or attempted coups since independence in 1975, four of those aided by French mercenaries.
The latest trouble began when Comoros' constitutional court said last week that Bacar's five-year term had expired, and ordered him to step down ahead of June elections.
Witnesses on Anjouan said on Friday that after two days of fighting, Bacar had regained control of the island, and his police had confiscated the arms and vehicles of a small government army contingent of about 30 soldiers.
Salim Miterand, a local photographer, said from Mutsamudu, Anjouan's capital: "Last night, police forces were driving round armed to the teeth. president Bacar wants to show the population he has won the battle."
Abourahim Said Bacar, a government spokesman, said: "Mohamed Bacar risks plunging Anjouan into civil war. The government is deeply worried at the climate of terror he has imposed."
The spokesman said the house of Ahmed Abdullah Mohamed Sambi, the national president, who hails from Anjouan, had been ransacked by police there.
First settled by Arab seafarers 1,000 years ago, and later a haven for pirates pillaging ships in the Indian Ocean, the rocky Comoros islands were annexed by France in 1904.
With a population of just over 800,000, the Comoros used to rely on exports of vanilla, cloves and ylang ylang oil.
But a slump in these commodities has left it increasingly dependent on remittances from abroad and donor aid.