At least 21 people have been killed and dozens wounded in northern Yemen, where Shi'ite Muslim rebels are attacking positions held by Sunni Islamist Salafi fighters with bursts of shelling, a spokesman for the Salafis said on Sunday.

The shelling, which killed three people on Saturday, continued on Sunday afternoon, he said, leaving a total of 21 dead and 48 wounded so far in the latest flare-up.

The conflict in the north, where government also troops tried to crush Shi'ite Houthi rebels before a cease-fire last year, is one of several plaguing Yemen which plans elections next year to replace President Ali Abdullah Saleh.

Saleh agreed this week to step down after 10 months of protests to end his 33-year rule.

The deputy to whom he transferred power, Abd-Rabbu Mansour Hadi, on Saturday set February 21 for the presidential election.

Yemen's neighbours, Washington and the United Nations, which echoed a Gulf power transfer plan in a Security Council resolution, hope a political process can halt a slide towards civil war in an impoverished country awash with weapons.

Regional powers, including world No. 1 oil exporter Saudi Arabia, fear a political vacuum in Yemen will embolden al Qaeda's Yemen wing.

Months of political paralysis over Saleh's fate have seen a shutdown in the oil industry Yemen depends on for export revenue, while conflict with a long-standing separatist movement and militant Islamists in the south have flared anew.

In recent weeks, the Houthis have clashed with Salafist fighters, leading local tribesmen to craft a truce between them. It seemed to collapse on Saturday, when Salafi spokesman, Abu Ismail, said Houthi fighters had shelled the town of Damaj.

Members of the Zaidi sect of Shi'ite Islam, the Houthi rebels led an uprising based in the northern Saada province that Saleh's forces struggled to crush, with Saudi Arabia intervening militarily in 2009 before a cease-fire took hold the next year.

The Houthis, who effectively control the northern Saada province, are deeply wary of Saudi Arabia's promotion of puritanical Sunni Salafi creeds that class Shi'ites as heretics.

Dayfallah al-Shami, a member of the Houthis' political office, disputed the Salafi account of the fighting. He told Reuters that leader, Abdelmalek al-Houthi, had issued orders for a cease-fire but that the Salafis rejected it and fought on.

We have martyrs and wounded, he said. We have informed the mediators that the Salafis can have their slogans as long as they refrain from incitement and takfir (denouncing a Muslim as an infidel).

(Writing by Joseph Logan; Editing by Louise Ireland)