France, Germany and Italy have all announced plans to evacuate their citizens while the UK has told its nationals to stay inside and changed its travel advice.
Mr Lammy said: “The situation in Niger is deteriorating rapidly following the recent coup, while the closure of Niger’s airspace is preventing British nationals from leaving by their own means.
“British nationals who want to get out of the country should now be supported by the Government to evacuate.”
Foreign nationals waited on Wednesday outside an airport in the capital, Niamey, for a French military evacuation flight while a regional bloc continued talks about its response to the junta.
Niger, a French colony until 1960, had been seen as one of the region’s last democracies and a partner Western countries could work with to beat back the jihadi violence that has wracked the Sahel region.
On Sunday, Ecowas, which stands for the Economic Community of West African States, said it would use force unless the president was released and reinstated within a week.
But juntas in neighbouring Mali, Burkina Faso and Guinea, also former French colonies, warned any forcible intervention would be seen as a declaration of war.
Mr Bazoum was democratically elected two years ago in Niger’s first peaceful transfer of power since independence from France.
Russian mercenary group Wagner is operating in Mali, and Vladimir Putin would like to expand his country’s influence in the region.