Yemen's government named a team of lawmakers on Sunday to oversee the military after four days of battles threatened to wreck a deal easing President Ali Abdullah Saleh from office.

At least two people were killed on Sunday in fighting between Saleh loyalists and opponents in the city of Taiz, centre of ten months of protests that have driven the Arab world's poorest country to the brink of civil war.

Sunday's deaths bring to at least 19 the toll since Thursday from fighting in Taiz in Yemen's south.

Vice-President Abd-Rabbu Mansour Hadi named the committee members who will oversee the end of fighting and the return of forces to barracks, state news agency Saba reported.

The opposition was not immediately available to comment on the composition of the committee which the two sides had agreed would include equal numbers from Saleh's General People's Congress (GPC) and the opposition Joint Meeting Parties (JMP).

The European Union has urged the government and opposition to agree quickly to a unity interim cabinet also.

The deal to remove Saleh was crafted by Yemen's richer Gulf Arab neighbours, which share U.S. fears a political and security vacuum will embolden the Yemeni branch of al Qaeda, and see multiple internal conflicts turn into full-blown civil war.

Saleh signed the deal last month after repeatedly balking, and it has been backed by the United Nations.

But implementation has bogged down over the formation of a government that would lead the country to a presidential election in February and the makeup of the body to run the military - key units of which are led by Saleh's relatives.

FIGHTING CONTINUES

Workers at a field hospital in Taiz, some 200 km (120 miles) south of the capital Sanaa, said a woman and child died from injuries suffered while trapped in a building hit by artillery fire.

The fighting eased later on Sunday. Gunmen from anti-Saleh factions held positions outside schools and government buildings - their windows shattered and their walls pocked with bullet holes - in a district of the city near where battles had raged.

Residents said on Saturday government forces had used artillery, tanks and rockets in residential areas of Taiz, trapping about 3,000 families during skirmishes with opposition fighters who responded with medium and light fire.

The province's governor was trying to negotiate a ceasefire between units loyal to Saleh - including the well-armed Republican Guard commanded by his son Ahmed - and his enemies.

There's no doubt that the army were responsible for some of the civilian deaths, Governor Hammound Khaled al-Soufi told reporters. Both sides shelled randomly into the city, that was a huge mistake.

One resident whose house was partly destroyed in the fighting said government forces had directed heavy fire on gunmen operating from residential areas.

The gunmen are using hit and run tactics, firing from houses and then fleeing, said Najib al-Muwadim.

Prime Minister-designate Mohammed Basindwa, an opposition leader, has warned his side would rethink its commitments under the transition deal if the fighting in Taiz did not stop.

Political crisis has frequently halted the modest oil exports Yemen uses to finance imports of basic foodstuffs, and ushered in what aid agencies deem a humanitarian crisis. More than 100,000 people have been displaced by military conflicts in both the north and south.

The EU envoy to the country, Michele Cervone d'Urso, told a news conference in the capital earlier on Sunday that he hoped to see the cabinet and military committee agreed within days.

It is time for Yemenis to see the benefits of a peaceful transition. They hope to see electricity and the dismantling of military checkpoints.

(Writing by Joseph Logan; Editing by Louise Ireland)