Warplanes from the coalition led by Saudi Arabia has bombed the residence of Ali Abdullah Saleh in the capital, Sanaa, but Yemen's former president is believed to be safe, witnesses have said.

Three air strikes hit Saleh's residence early on Sunday morning, but the president and his family are "well", Yemeni news agency Khabar said, according to the Reuters news agency.

Plumes of smoke were seen rising from the area in the latest strike in Sanaa following a night of intensive air raids against rebel positions after rebels shelled Saudi border town on Thursday.

Saleh, who stepped down in 2012 following a year of deadly nationwide protests against his three-decade rule, is accused of siding with Houthi fighters who ousted UN-backed President Abd-Rabbu Mansour Hadi in February.

Air strikes against the Houthis and fighters allied to Saleh have been carried out by a coalition of Arab nations since March 26.