Treasury Secretary Steven Mnuchin in recent days urged U.S. suppliers of Huawei Technologies Co. to seek licenses to resume sales to the blacklisted Chinese firm, according to people familiar with the situation.

The development reflects a recent reversal of the Trump administration’s get-tough stance on Huawei, amid continuing rifts among officials over how far the U.S. should go in trying to reach an accord with Beijing. Huawei’s pariah status in the U.S. has become a stumbling block in trade talks with China.

Mr....