The US State Department on Thursday announced a withdrawal of non-emergency staff and their families from its embassy in Niger's capital Niamey because of instability after the coup.
"Given ongoing developments in Niger and out of an abundance of caution, the Department of State is ordering the temporary departure of non-emergency US government personnel and eligible family members from the US embassy in Niamey," spokesman Matthew Miller said in a statement.
It was the seventh military takeover in less than three years for the West and Central Africa region.
On Wednesday, US Secretary of State Antony Blinken spoke with Mr Bazoum by phone, Mr Miller said in a separate statement.
"We reiterate that the safety and security of President Bazoum and his family are paramount," he said.
"The United States is dedicated to finding a peaceful resolution that ensures that Niger remains a strong partner in security and development in the region."
Earlier, Mr Miller said the evacuation was to protect "safety and security" of US citizens and government staff while "commercial flight options are limited".
France sent its first evacuation flight on Tuesday, on which people from several European states travelled. It has since sent two more, and a fourth is reportedly planned.
An Italian military plane with 99 passengers arrived in Rome from Niger on Wednesday and other countries are considering sending flights for additional nationals seeking to leave Niger.
The US embassy will continue to be "open for limited, emergency services for US citizens", Mr Miller said, while the government's travel advisory has raised its threat level to "Do not travel".
"We are only able to provide emergency assistance to US citizens in Niger given our reduced personnel."
The US has said it is in communication with military members now leading the country, and its newly appointed ambassador Kathleen FitzGibbon is set to arrive in Niamey soon.
"The United States remains committed to our relationship with the people of Niger and to Nigerien democracy," Mr Miller said. "We remain diplomatically engaged at the highest levels."