In May 2019, a top official in the U.S. Department of Agriculture got a call on his cellphone from Senator Robert Menendez of New Jersey.

The conversation was brief, the senator was curt, and the message was clear: “Stop interfering with my constituent.”

Ted A. McKinney, then the under secretary for trade and foreign agricultural affairs, testified about the exchange on Friday during the third week of Mr. Menendez’s bribery trial in Federal District Court in Manhattan.

It was the first time that jurors had heard directly from a witness who attributed conduct to the senator that is central to the government’s claim in an indictment that alleges a sprawling bribery conspiracy: that Mr. Menendez was willing to flex his political muscle to win favorable treatment for allies.

In exchange, prosecutors say, Mr. Menendez and his wife were rewarded with bribes including gold, wads of cash and a Mercedes-Benz convertible.

At the time of the call, Mr. McKinney and others at the U.S.D.A. had been publicly sounding the alarm about a deal Egypt had brokered that granted a halal meat monopoly to a New Jersey startup run by Wael Hana, a longtime friend of the senator’s wife, Nadine Menendez.