(CNN) -- The U.S. State Department on Thursday recommended that all non-emergency staff and their families at the U.S. Embassy in Yemen leave the country after an attack on the building that killed 11 people, including one American.
Wednesday's attack by suspected al Qaeda-linked insurgents killed six Yemeni police and four civilians when the attackers, disguised as Yemeni forces, bombed the outer wall of the embassy and opened fire on first responders, said Mohammed al-Basha, a spokesman for the Yemeni Embassy in Washington.
Six attackers -- including one wearing a suicide vest -- were also killed, al-Basha said. Yemeni forces have rounded up at least 30 suspects, a security official said.
On Thursday, U.S. State Department spokesman Robert Wood reported that an American was among the dead as well. Watch more about the attack »
"We are saddened to confirm that among the victims of yesterday's terrorist attack against our Embassy in Sanaa, Yemen, was Susan El-Baneh, an American citizen."
El-Baneh, 18, of Lackawanna, New York, had just been married and was visiting family in the Yemeni capital. Her husband, a Yemeni national, also died in the attack, Wood said.
The State Department's directive to non-emergency staff followed a similar warning in April, after after attacks against the embassy and a residential compound. That order was lifted last month, but has been reinstated since Wednesday's attack.
In a travel warning issued Thursday, the State Department said it would not authorize any travel outside the capital city of Sanaa, and asked U.S. citizens to defer all non-essential travel into the country. Those choosing to remain in Yemen were asked to "exercise caution" -- be vigilant, avoid crowds, keep a low profile, and vary times and routes for travel.
"The Department remains concerned about possible attacks by extremist individuals or groups against U.S citizens, facilities, businesses, and perceived threats," it said.
Diplomatic sources told CNN Thursday they are aware of the reports. They noted that usually after such incidents, Yemeni security forces cast a broad net "bringing in the usual suspects, and then nothing comes out of it."
Meanwhile, Yemen's president has condemned the embassy attack and vowed to pursue the "criminals" who carry out such acts, The Associated Press reported the country's news agency as saying Friday.
In his first remarks since Wednesday's assault, President Ali Abdullah Saleh lashed out against terrorists, saying their actions are a result of "faulty upbringing."
"Security forces cannot prevent a terrorist from dying because he has decided to die, and this is a result of an ignorant and backward mind-set," the president was quoted by SABA as saying late Thursday in the town of Hodeida. "They offer no plans to serve the country; their plans are just death and destruction."
The embassy temporarily closed after the Wednesday morning attack so staff could help Yemeni investigators. It plans to resume normal operations on Saturday, after the normal weekend in Yemen.
The attackers detonated two car bombs in an attempt "to breach the wall ... and then have the attackers go on foot through this breach in the wall," State Department spokesman Sean McCormack said.
"The attack bears all the hallmarks of an al Qaeda attack," he added.
Yemen also believes al Qaeda is responsible, al-Basha said.
Media reports said Islamic Jihad in Yemen -- which is affiliated with al Qaeda -- has claimed responsibility for the attack.
The U.S. State Department had previously warned of violence that it attributes to Islamic extremists in Yemen.
In March, three mortar rounds landed near the embassy, wounding Yemeni students at a nearby school and Yemeni government security personnel, the State Department said.
The next month, an expatriate residential compound in the Hadda neighborhood was attacked by mortar fire. Suspected extremists fired two mortar rounds toward the Yemen Customs Authority and Italian Embassy in April, as well, but no one was hurt.
-- CNN's Elise Labott and Diane Ruggiero in Washington and Schams Elwazer and Ben Wedeman in Sanaa contributed to this report.