The US has ordered all its non-essential diplomats and family members of embassy staff to leave Yemen as fighting there escalates.
Medical sources say 72 people have died in three days of clashes between tribal fighters and government troops.
President Ali Abdullah Saleh has again said he will not step down, despite mounting protests.
He has so far refused to sign a transition deal that would see him resign in favour of a unity government.
The US has repeated its call for Mr Saleh to step down, urging all sides to accept a ceasefire.
"We continue to support the departure of President Saleh who has consistently agreed that he would be stepping down from power and then consistently reneged on those agreements," Secretary of State Hillary Clinton told reporters in Paris.
The UK Foreign Office has strongly advised all British nationals to leave Yemen immediately as fighting there escalates.
It said its ability to provide consular assistance was limited, and airports and routes in and out of Sanaa and other cities may be closed.
In its travel advisory, the US state department said there was "ongoing civil unrest throughout the country and large-scale protests in major cities".
Fighters from a powerful tribal group, the Hashid, are said to have taken control of several public buildings in the capital Sanaa after several days of fighting government troops.
Sanaa's airport was temporarily closed on Wednesday as tribal fighters clashed with government forces.
"The Department of State has ordered all eligible family members of US government employees as well as certain non-emergency personnel to depart Yemen. US citizens currently in Yemen should depart while commercial transportation is available."
The UK Foreign Office has advised against all travel to Yemen since April, urging any British nationals in the country to leave.
Civil war warning
Hundreds of people have been fleeing the violence in the capital, where fighting continuing on Thursday.
"There are still sporadic artillery hits and gunfire in Sanaa," said Jeb Boone, managing editor of The Yemen Times.
"We don't know whether tribesmen are forcing their way into the city or whether the government forces are pushing them out," he told the BBC.
The clashes began on Monday after forces loyal to President Saleh moved against the compound of Hashid leader Sheikh Sadiq al-Ahmar.
Medical sources told the BBC that 54 people - including Ahmar supporters, women and children - had died in fierce fighting, as well as 18 government soldiers.
More than 250 people have reportedly been injured.
Yemen's defence ministry said 28 people were killed when a munitions factory belonging to the Ahmar tribe exploded.
While Mr Saleh has ordered the arrest of "rebellious" Mr Ahmar and nine of his brothers, the Hashid leader says he is in a "position of strength" and prepared to fight "until the end".
In a defiant interview with Arabic network al-Jazeera on Thursday, he repeatedly called Mr Saleh a liar, accusing him of fomenting a civil war and repeatedly calling for him to step down.
Mr Ahmar said he was being protected by army soldiers as well as his tribesmen, and was holding 70 soldiers who had surrendered as prisoners.
He added: "I am prepared to stop this war if Ali Abdullah Saleh does so too."
Mr Saleh has so far refused to stand down, despite growing international pressure, warning that Yemen could descend into civil war.
In a statement on Wednesday he said he was prepared to sign a transition deal "within a national dialogue and a clear mechanism".
The deal Mr Saleh has so far refused to sign, which was presented by the Gulf Co-operation Council, calls for him to step down within a month after 33 years in office and hand over power to a unity government.
It would also give the president immunity from prosecution.