The US is stepping up efforts to persuade Yemen's veteran president to step down before escalating fighting between the government and tribal rebels develops into civil war.

Diplomats said on Thursday that Washington was now pressing hard to convince Ali Abdullah Saleh to reconsider his rejection of a peace plan brokered by Saudi Arabia and other Gulf states alarmed by the prospect of growing instability in the region.

John Brennan, Barack Obama's counter-terrorism adviser, held talks in the Saudi capital, Riyadh, where the government has strong ties with Yemeni tribes but has been slow to act.

It has been accused of sending mixed signals to Saleh, who is seen as desperate to cling to power after 32 years.

Brennan has previously worked closely with Saleh on fighting al-Qaida – a key US and western concern. The Yemeni leader has reneged on an accord that would see him hand over power to his deputy in return for an amnesty from prosecution.

He has agreed to sign the deal on several occasions but then backed out, apparently holding out for terms that would wring new concessions from his rivals.

The official Yemeni news agency Saba quoted a government source on Thursday as saying that he was now ready to sign, but the claim appeared to make little impact.

"It's all about getting him to sign that piece of paper," said one western official. "It's the only game in town but he clearly hasn't grasped that yet."

Reports from Sana'a said Saleh's forces were deploying heavy weapons at the entrance to the capital city to prevent the advance of rebels loyal to Sheikh Sadiq al-Ahmar, chief of the Hashid tribal federation, the country's largest. At least 135 people have been killed in the last 10 days.

The situation in Yemen remains confused and communications are difficult. Al-Jazeera TV reported that an estimated 2,000 members of opposition tribal groups, which were "armed and ready to fight", had entered the capital to confront forces loyal to Saleh.

"We expect [the tribal fighters] to take control of government complexes," said the editor of the Yemen Post, Hakim al Masmari.

A military official told the Associated Press that government warplanes would attack the fighters if they tried to advance on the capital.

"There are orders that if they approach and engage, we can strike them with airplanes," the official said, speaking on condition of anonymity according to regulations.

For their part, the tribesmen said they were awaiting orders to approach. "We won't leave [Hamid] al-Ahmar alone and will enter Sana'a to stand with him and to fight alongside him," Mohammed al-Hamdani, a tribal leader, told AP.

Video clips showed heavy fighting in the Hasaba area, where 15 people were killed overnight. One casualty was a seven-year old girl struck by a stray bullet.

Sana'a international airport was closed because of shelling, fuelling fears the country would be cut off from the wider world. But it reopened later as the authorities insisted all was normal.

The US and Britain have advised their nationals to depart and their embassies are both operating with reduced staff.

A Yemeni government official said street fighting had intensified because special forces were now involved.

Civilians have been fleeing Sana'a in their thousands. "It felt as if the artillery shells were flying next to my head," resident Sadeq al-Lahbe told Reuters before leaving.

"My wife, my daughter were screaming. It was horrible. There is no electricity, no water and violent strikes shaking the house. Is this life?"

In the central city of Taiz, where anti Saleh activists have held demonstrations since the start of the uprising, military police were seen firing live ammunition at protesters. The UN said at least 50 people had been killed there since Sunday.

The battles in Yemen are being fought on several fronts, with street fighting between tribal groups and Saleh's forces in Sana'a, popular protests across the country, and a battle against al-Qaida and Islamist militants who have seized the coastal city of Zinjibar, east of Aden. Government forces have been pounding the city for several days.

Brennan's Gulf mission followed mounting alarm and frustration in Washington and London at the way the crisis was unfolding.

On Wednesday the US secretary of state Hillary Clinton said: "We cannot expect this conflict to end unless President Saleh and his government move out of the way to permit the opposition and civil society to begin a transition to political and economic reform."