Yemeni President Abdrabuh Mansur Hadi Friday urged Shiite rebels who overran Sanaa at the weekend to pull out of the capital, accusing them of breaching a UN-brokered peace accord.

Hadi's call came as Washington ordered a cut in the number of American government staff in Yemen due to the "unpredictable" security situation, and an updated travel advice urged US citizens in Yemen to leave.

The Huthi rebels, who had besieged Sanaa for a month, seized key state installations Sunday without any resistance, after clashes on the city's outskirts with Islamists from the Sunni Islah party and tribes killed more than 270 people.

Hadi has so far failed to name a new prime minister as stipulated by the agreement to end the fighting, which was mediated by UN envoy Jamal Benomar and signed hours after the rebel takeover Sunday.

"The legitimate way to implement this agreement is to recognise the state's authority over the whole country, especially Sanaa," President Hadi said in an address to the nation.

"All installations and stolen weapons should be handed" back to the authorities, he said, referring to scores of tanks and armoured vehicles rebels seized when they stormed army bases.

"Settling accounts by force and acts of vengeance will not build a state," Hadi said, addressing the rebels who had organised protests demanding the ouster of the government which they accused of corruption.

"Does fighting corruption and state-building come through pillaging houses, miliary bases and government institutions," asked the president.

A security protocol to the accord would have required the rebels to hand over the institutions they seized and start dismantling their armed protest camps in and around Sanaa once a new premier is named.

But rebel representatives refused to sign it.

President Hadi defended the deal without providing a clear reason for the lightning collapse of resistance.

"We were let down by those who put their interests above those of the homeland... those who abandoned their responsibilities and commitments," he said.

Hadi appeared to be referring to backers of former president Ali Abdullah Saleh, who stepped aside in February 2012 after a year of Arab Spring-inspired protests, but whose party still controls half of the government.

Hadi was expected to name a new premier by Wednesday, but lack of agreement on a candidate has prevented him, observers said.

He has already appointed himself two advisers, one representing the rebels, and another for southern separatists, as required under the peace deal.

The agreement should be implemented "without procrastination" in order to advance towards a "civil and modern state, based on justice, equality and partnership," said Hadi.

On Friday, thousands of Huthi supporters gathered for weekly prayers near a main protest camp on Airport Road in Sanaa, where the imam hailed the rebel "victory," an AFP correspondent reported.

Shiite rebels banned Sunni clerics close to Islah from delivering the Friday sermon in various mosques in Sanaa and replaced many with others from their own ranks, residents said.

These include the main mosque of Zee al-Nurayn, where top Islah cleric Abdulmajeed al-Zindani, who has gone into hiding, usually leads the prayers.

The rebels maintained a strong security presence in the northern neighbourhoods of the capital, home to most government buildings and ministries, with patrols of armed men roaming the districts.

But their presence remained minimal in the southern neighbourhoods of Sanaa, and were nowhere to see in the streets leading to the presidential complex.

Speaking in Washington, State Department spokeswoman Jen Psaki said the decision to reduce staffing stemmed from "an abundance of caution and in response to recent political developments and the changing, unpredictable security situation."

But she stressed that the US embassy has not suspended operations "and will continue to operate, albeit with reduced staff."

Yemeni authorities have repeatedly accused Iran of backing the rebels, who also appear influenced by Lebanon's powerful Shiite militia Hezbollah, which is supported by Tehran.

Sunday's deal is aimed at putting the troubled transition since Saleh's ouster back on track in impoverished Yemen, which borders oil kingpin Saudi Arabia and is a key US ally in the fight against Al-Qaeda.