The State Department on Tuesday told American citizens and others looking to get out of Afghanistan that they should "shelter in place" until they are given further instruction by the U.S. Embassy amid a fragile security situation in the Afghan capital.

"Our message remains for American citizens and for others who have expressed interest in relocation out of Afghanistan: shelter in place until and unless you receive a communication from the U.S. embassy," spokesman Ned Price told reporters.

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He said the department had notified the first batch of Americans overnight who had "expressed interest in being repatriated" with specific information about where to go and when to go there.

The advice comes as the U.S. scrambles to get Americans and U.S. allies out of Kabul as quickly as possible as the Taliban secure their control of the falling Afghan capital. 

Flights were temporarily suspended from Kabul's airport on Monday, as U.S. forces attempted to gain control of the crowd of Afghans desperate to leave the country. A White House official told Fox News Tuesday that military and civilian flights from Hamid Karzai International Airport in Kabul have resumed, and that over the last 24 hours the U.S. has been able to move more than 700 people out of Afghanistan, including 150 American citizens. 

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However, a former State Department contractor told Fox News that Taliban fighters have established checkpoints throughout the city and around the airport. Some, he said, are beating people on the way to the airport. 

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Sources have also told Fox News that the Taliban are going through neighborhoods looking for those who worked with the U.S. government. 

On Tuesday, Price emphasized that "this is, again, a challenging security environment" and reiterated that individuals should remain in place until told to move.

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Earlier, he said the U.S. had "received assurances from the Taliban that they will allow safe passage for civilians transiting to the airport."

"We take it for what it is," he added, noting who it was that was making those assurances. "We will, of course, be looking for one thing and one thing only – follow through."

Fox News' Brooke Singman and Rich Edson contributed to this report.