ADEN, Yemen, April 8 (Reuters) - Dozens of Yemeni Houthi fighters clashed with local militiamen in the central Aden district of Crater on Wednesday and mosques broadcast calls for jihad to combat the Houthi forces trying to take over the southern Yemeni port city, residents said.

They said several houses were on fire after being hit by rockets, and families stayed indoors as fighting raged from street to street.

The Houthis, who are allied to soldiers loyal to former president Ali Abdullah Saleh, advanced into Crater on Wednesday morning with a tank and two armoured vehicles, one resident said.

Mosques in Crater called on the population to wage holy war against the Houthis, their loudspeakers, usually reserved for sermons and the call to prayer, broadcasting: "God is the greatest! Rise for jihad!"

The battle in the old centre of Aden came a day after fighters from the city said they had pushed the Houthis and allied troops from positions in northern Aden neighbourhoods, which they said cut Houthi supply lines into the centre.

One fighter, Yasser Mahmoud, said the Houthis had been pushed from the Dar Saad neighbourhood at the northern approach to Aden. He said 22 Houthi fighters were killed when a tank and an armoured vehicle were destroyed.

Three explosions shook northern areas of Aden on Wednesday, in what residents said were air strikes by the Saudi-led coalition which is two weeks into a campaign to stem Houthi advances. They said the attacks appeared to target weapons depots.

(Reporting by Mohammed Mukhashaf; Writing by Dominic Evans; Editing by Raissa Kasolowsky)