The Trump administration secretly reached out to Iran in December to propose creating a direct channel to negotiate the release of prisoners held by each side, U.S. officials and people briefed about the discussions said, marking the first U.S. diplomatic overture to Iran on the issue under President Donald Trump.

However, Iran didn’t respond and, despite at least three subsequent offers from Washington, so far has refused to engage with U.S. officials on the offer, the people briefed on the discussions said. The apparent...