WASHINGTON — The United States escalated its war against the Islamic State in Libya on Monday, conducting airstrikes in the coastal city of Surt as part of a new military campaign against the extremist Sunni terrorist group’s stronghold in North Africa.

President Obama approved the strikes last week after Libya’s fragile United Nations-backed unity government asked for help in its fight against the Islamic State, administration officials said.

The strikes, which American officials have forecast for months, are intended to help break an impasse between Libyan militias and the Islamic State fighters they have cornered in a grinding urban battle in Surt’s downtown.

American officials, who estimate that there are fewer than 1,000 Islamic State fighters in Surt, say that American warplanes could provide a decisive advantage to the attackers and help break the stalemate along the fighting fronts in the southern and western part of the city. But they also say that the Islamic State’s modest numbers in Surt belie their determination, if not desperation, and that with escape routes from Surt largely cut off, the Islamic State fighters may fight to the death.