A long-running dispute between Huawei Technologies Co. and a small U.S.-based contractor has escalated to U.S. federal court, with the contractor alleging Huawei stole its technology and pressured it to build a “back door” into a sensitive law-enforcement project in Pakistan.

The contractor, Buena Park, Calif.-based Business Efficiency Solutions LLC, or BES, says in a lawsuit filed Wednesday in California district court that Huawei required it to set up a system in China that gives Huawei access to sensitive information about citizens and government officials from a safe-cities surveillance project in Pakistan’s second-largest city of Lahore.

Muhammad Kamran Khan, chief operating officer of the Punjab Safe Cities Authority, which oversees the Lahore project, said the authority has begun looking into BES’s allegations.

“Our team is examining the accusations and sought an explanation from Huawei,” Mr. Khan said in an interview. “We have also put a data security check on Huawei after this issue.”

“So far, there has been no evidence of any data stealing by Huawei,” he said.