WASHINGTON — President Trump is considering reversing major pieces of the Obama administration’s opening with Cuba and reinstating limits on travel and commerce, citing human rights abuses by the Castro government as justification for a more punitive approach.

Mr. Trump wants to announce the changes in Miami as early as June and deliver on a campaign promise that remains a cherished demand for the politically conservative Cuban-American exile community, according to aides who spoke on the condition of anonymity. But he has not made a final decision on the steps he will take because of internal disagreements within his administration over how far to go in unwinding one of President Barack Obama’s most significant foreign policy achievements.

Clamping down on engagement with Cuba would be a high-profile way for Mr. Trump to showcase a stark break with his predecessor and to fulfill a pledge, delivered during a speech in Miami in September, to a crucial constituency that disproportionately supported him. It would also enable the president to reward the loyalty of Cuban-American lawmakers who have been agitating for a harder line on Cuba, including Senator Marco Rubio and Representative Mario Diaz-Balart, both Republicans of Florida.

But as the White House has sought to formulate a series of steps for Mr. Trump to announce, a split has emerged over rolling back a policy that many senior officials privately agree has been an improvement on the Cold War dynamic that shaped relations with Cuba in the past. In addition to the revival of diplomatic relations for the first time in a half-century and liberalized rules for trade, travel and commerce, the new approach has paved the way for cooperation in intelligence-sharing, drug interdiction, scientific research and a host of other areas.