The U.S. embassy there remains open as of now.
A State Department spokesperson told ABC News that officials are "continuing to closely monitor developments in Yemen and will adjust the embassy’s security posture response in accordance to the situation on the ground."
"The embassy has been operating with reduced staffing and heightened security since going on ordered departure on September 24, 2014," the spokesperson said. “We are deeply concerned about the turn of events in Yemen over the last few days, including the ongoing attack on the Presidential palace, and call for immediate cessation of hostilities."
In recent days, Houthi tribal fighters have moved into the capital of Sanaa and surrounded key government buildings, including the Presidential Palace, U.S. officials said. The whereabouts of President Abed Rabbo Mansour Hadi remain unknown.
The amphibious ships USS Iwo Jima and USS Fort McHenry moved on Monday night from the Gulf of Aden to the southern Red Sea, placing them closer to Sanaa should they be needed, the defense official said.
The embassy has been operating at reduced staffing levels for some time, as only essential personnel are allowed to work there, the official said, noting that the U.S. embassy in Sanaa has a large force of more than 100 Marines permanently assigned there to provide security.
At least twice over the past year, the State Department has ordered non-essential U.S. embassy personnel in Yemen to leave the country, most recently in November. Those personnel left the country via commercial aircraft.
But the U.S. military has also been called on to assist with the departure of embassy personnel as occurred in August 2013, when non-essential embassy personnel were evacuated aboard an Air Force C-130 transport aircraft.
Two U.S. officials confirmed to ABC News that a U.S. embassy vehicle was shot at in Sanaa on Monday near the U.S. embassy. No one was injured in the attack and it remains unclear who was responsible for the attack. One official indicated that the international airport in Sanaa remains open -- a key option if a decision is made to move personnel out via commercial aviation.
ABC News' Kirit Radia, Justin Fishel and Arlette Saenz contributed to this report.