The State Department on Wednesday ordered nonessential U.S. diplomats to depart Yemen and urged all Americans there to leave as security conditions deteriorated, with the country's embattled leader refusing to step down.

The decision to tell most nonessential personnel and the families of all American staff at the U.S. Embassy in Sanaa to leave was a sign of Washington's increasing concern about the situation in Yemen, where street battles between supporters and opponents of Yemeni President Ali Abdullah Saleh raged for a third day. The clashes have left at least 41 dead and dozens badly injured.

"The security threat level in Yemen is extremely high due to terrorist activities and civil unrest," the State Department said in its advisory. "There is ongoing civil unrest throughout the country and large-scale protests in major cities."

It noted that violent clashes were occurring in Sanaa, the capital, and "may escalate without notice."

The "ordered departure" notice came in a new travel warning for Yemen released as the Obama administration stepped up calls for Saleh to transfer power under an agreement negotiated by neighboring Gulf states.

Speaking in London earlier Wednesday, President Barack Obama called on Saleh to "move immediately" to implement the agreement. Saleh has balked three times at following through on verbal commitments to step down.

The earlier U.S. travel alert for Yemen issued in March had allowed nonessential embassy staff and their families to leave at government expense. It had also urged Americans not to go to Yemen but had only told those already in the country to consider leaving.

The new alert followed a defiant message from Saleh, who vowed not to step down or allow Yemen to become a "failed state." His stance, combined with renewed fighting, sharply increased chances that Yemen's three-month uprising could turn into a militia-led revolt after Arab mediation failed to crack Saleh's 32-year authoritarian rule.

"I will not leave power and I will not leave Yemen," a spokesman, Ahmed al-Soufi, quoted Saleh as saying.

He also took a direct swipe at U.S.-backed efforts to negotiate his exit. "I don't take orders from outside," said Saleh's statement, read by the spokesman in a meeting with tribal allies.

"Yemen will not be a failed state. It will not turn into an Al Qaeda refuge," the statement added in another stab at Western fears that chaos in Yemen would open the door for an Al Qaeda offshoot to expand its operations. The Yemen-based cell, Al Qaeda in the Arabian Peninsula, is linked to the attempted Christmas Day 2009 bombing of an airline over Detroit and explosives found in parcels intercepted last year in Dubai and Britain.

Despite his tough talk, Saleh's statement also promised he would try to keep the latest violence from "dragging the country into a civil war."

The clashes began Monday after Saleh's troops tried to storm the compound of the head of Yemen's largest tribe, the Hashid. Hundreds of tribal fighters then responded with fierce attacks on government forces.