US President Donald Trump offered to destroy the career of a state senator who was criticised by a sheriff during a meeting at the White House.

Discussing drug traffickers, Sheriff Harold Eavenson, of Rockwell County, Texas, mentioned a senator whose actions he disagreed with.

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Eavenson told the meeting: "A state senator in Texas was talking about introducing legislation to require [a] conviction before we could receive forfeiture money" from drug traffickers.

"I told him that the cartel would build a monument to him in Mexico if he could get that legislation passed," he added, in comments carried by Business Insider.

"Who is the state senator? Do you want to give his name? We'll destroy his career!" Trump said, prompting laughter in the meeting.

Eavenson, speaking with the media following the meeting, refused to name the senator that he was referring to – having also refused to do so in the meeting – and said Trump was clearly joking when he made the remark.

Trump also used the meeting to reiterate his commitment to dealing with crime and criminals, again stating that he is determined to have a wall built on the country's border with Mexico to stem the flow of drugs into the US.

"We're committed to securing our borders," he said, in comments carried by The Hill. "We're going to be building a wall."

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