Venezuelan officials, hoping to end their country’s clash with the United States, offered the Trump administration a dominant stake in Venezuela’s oil and other mineral wealth in discussions that lasted for months, according to multiple people close to the talks.

The far-reaching offer remained on the table as the Trump administration called the government of President Nicolás Maduro of Venezuela a “narco-terror cartel,” amassed warships in the Caribbean and began blowing up boats that American officials say were carrying drugs from Venezuela.

Under a deal discussed between a senior U.S. official and Mr. Maduro’s top aides, the Venezuelan strongman offered to open up all existing and future oil and gold projects to American companies, give preferential contracts to American businesses, reverse the flow of Venezuelan oil exports from China to the United States, and slash his country’s energy and mining contracts with Chinese, Iranian and Russian firms.

The Trump administration ended up rebuffing Mr. Maduro’s economic concessions and cut off diplomacy with Venezuela last week. The move effectively killed the deal, at least for now, the people close to the discussion said.

Though the United States has been targeting what it calls drug boats, the cutoff of diplomacy, the military buildup near Venezuela and the increasingly strident threats against Mr. Maduro by Trump administration officials have led many in both countries to think that the Trump administration’s real objective is Mr. Maduro’s removal.