Chilean lawmakers have once again delayed voting on a major Pacific trade deal, heightening concerns that they could reject the treaty.

Deputies in Chile’s lower house were scheduled to vote on the Comprehensive and Progressive Agreement for the Trans-Pacific Partnership April 2, but agreed at the start of the session to send the legislation on ratification to the Chamber of Deputies’ Constitutional Committee for further consideration.

Some sources said the vote could take place next week, but Hernan Miranda, coordinator...