The United States, Britain and France rushed to close their embassies over security fears in Yemen, with US staff destroying top-secret documents and abandoning vehicles at the airport.

The hasty exit came as thousands joined rival demonstrations over last week's Shiite militia takeover, which was widely condemned as a coup.

Long on the front line of the US war against Al-Qaeda, Yemen has descended into chaos since the militia, known as Huthis, seized the capital Sanaa in September and ousted the parliament last week.

The United Nations has demanded the reinstatement of the Western-backed leader Abedrabbo Mansour Hadi -- who resigned last month and is under effective house arrest -- but its efforts to broker a deal have failed so far.

After weeks of internal deliberations and drawing down staff, Washington finally closed its Sanaa embassy over the "deteriorating security situation," evacuating staff to Muscat late Tuesday on a private Omani jet.

State Department spokeswoman Jen Psaki thanked Oman's sultan for his help as well as Qatar, saying most staff were now en route back to Washington.

All the US Marines also left the country, taking commercial flights. Officials stressed that there were still US special forces on the ground to carry on the fight against Al-Qaeda.