HOUSTON — A comment President Trump made on Tuesday in which he spoke of destroying the career of a Texas state senator has angered Democratic lawmakers in the state and cast a spotlight on the issue that set off the remark — the seizing of suspects’ property by law enforcement before those suspects have been convicted of a crime.

Mr. Trump’s remark came during a meeting at the White House with sheriffs from around the country. At one point, the president asked the sheriffs seated at a table around him if there were any pressing law enforcement issues they wanted to talk about.

A Texas sheriff, Harold Eavenson of Rockwall County, spoke up.

“Mr. President, on asset forfeiture,” Sheriff Eavenson said, in an exchange that was observed by reporters and filmed, “we’ve got a state senator in Texas that was talking about introducing legislation to require conviction before we can receive that forfeiture money, and I told him that the cartel would build a monument to him in Mexico if he could get that legislation passed.”

“Can you believe that?” Mr. Trump responded, then added, “Who’s the state senator?”

Sheriff Eavenson did not reply. “Do you want to give his name?” Mr. Trump said. “We’ll destroy his career.” Laughter then broke out.