Yemeni President Ali Abdullah Saleh has moved a step closer to handing power to his deputy by accepting a U.N. formula to ease a transition and end an uprising against his rule, the EU envoy to Yemen was quoted by the state news agency Saba as saying.

Heavy fighting between Saleh's supporters and opponents spread through Yemen's third-largest city of Taiz, some 200 km (120 miles) south of the capital Sanaa, killing four people and wounding 40 on Wednesday, a doctor there said.

Saleh, 69 and in power for 33 years, has three times agreed to give up power, only to pull out at the last minute, defying hostile demonstrations inspired by protests across the Arab world.

Michele Cervone d'Urso, the European Union resident ambassador, was quoted by Saba as saying he believed the Yemeni leader had now accepted a U.N. transition plan.

We are convinced that we are on the verge of reaching an agreement soon and above all else the matter calls for political commitment. We hope that Eid al-Adha (Muslim holiday) will be an occasion to announce to Yemen and the world that Yemen has passed towards a new stage, d'Urso told Saba.

D'Urso asked the opposition to return home before the holiday next week, so that a deal could be finalised. Opposition leaders are in Kuwait to drum up support for their movement.

A spokesman for a Yemeni opposition council treated the development with caution. We heard good things from the diplomats, but actions speak louder than words. We are not optimistic right but if the Gulf initiative is signed we will be more optimistic, said Houriya Mashhur.

Ruling Yemen since 1978 through a civil war and rebel movements, Saleh has clung to power despite an assassination attempt that sent him abroad for three months for medical care, breakaway generals and nine months of street protests.

Neighbouring oil giant Saudi Arabia and the international community fear growing lawlessness in Yemen is giving al Qaeda's regional wing scope to plan and potentially launch attacks in the region and beyond.

In Taiz, fighting raged between government troops and dissident army units on the city's main street. A local source said a bank had been attacked and looting had broken out.

SMALL STEPS

There was no immediate Yemeni government reaction on d'Urso's remarks. But there have been indications of progress.

Deputy information minister Abdo al-Janadi said on Sunday the ruling party was close to announcing Vice President Abd-Rabbu Mansour Hadi would succeed Saleh.

He said Hadi would return from the United States on Thursday to wind up dialogue with the opposition. He added: He will sign the Gulf initiative and the mechanism for its operation in the near future.

U.N. envoy Jamal Benomar visited Yemen in September to try to devise a way of implementing a Gulf-brokered power handover and overcome political deadlock that has paralysed the Arabian Peninsula state and pushed it to the verge of civil war.

But he left empty-handed after two weeks of shuttle diplomacy between the opposition and the ruling party.

Benomar's plan requires Saleh to shift power to Hadi ahead of an early presidential election, which would be held within two to three months. In the meantime, the opposition would form a government with the ruling party and a body would be set up to restructure the armed forces.

But Yemeni protest leader Tawakul Karman, who was awarded the Nobel Peace Prize along with two Liberian women last month said the deals on the table offered too little, too late.

It is disgraceful that the few who claim to show an interest in the future of Yemen should be satisfied with proposing initiatives, the most outrageous of which is to give complete immunity to Saleh, his sons and senior aides from any accountability for the crimes they have committed, including the killing of hundreds of revolutionaries, she wrote in Britain's Guardian newspaper.

(Reporting by Mohammed Ghobari; Writing by Isabel Coles; Editing by Maria Golovnina)