The Trump administration is pursuing a deal to sell nuclear reactors to Saudi Arabia despite the kingdom’s refusal to accept the most stringent restrictions against the proliferation of nuclear weapons, U.S. officials say.

Saudi Arabia’s nuclear energy ambitions could open a new market worth tens of billions of dollars, drawing countries including Russia, South Korea and China to compete for the business. Administration officials consider it too important to overlook, especially when the U.S. nuclear power industry is on the...