Senator Robert Menendez of New Jersey, a powerful Democrat who once led the Senate Foreign Relations Committee, was convicted on Tuesday of participating in a vast international bribery scheme, in which prosecutors said he had accepted gold, cash and other payoffs worth hundreds of thousands of dollars in exchange for political favors abroad and at home.

A Manhattan jury returned the verdict after deliberating for about 13 hours over three days in Federal District Court. Mr. Menendez was found guilty on all 16 counts he faced, including bribery, honest services wire fraud, extortion, obstruction of justice, conspiracy and acting as an agent for Egypt.

The verdict made Mr. Menendez the first United States senator to be found guilty of acting as an agent of a foreign power and the seventh to be convicted of a federal crime while in office.

Mr. Menendez, 70, now faces the possibility of many years in prison when he is sentenced by the judge, Sidney H. Stein. Eight of the counts on which he was convicted carry potential 20-year sentences. The judge said he would sentence Mr. Menendez on Oct. 29.

The resounding verdict will almost certainly deliver a final blow to Mr. Menendez’s storied four-decade political career and create intense pressure for him to leave office before his term expires at year’s end. Senator Chuck Schumer, the New York Democrat and majority leader, said in a statement, “In light of this guilty verdict, Senator Menendez must now do what is right for his constituents, the Senate and our country, and resign.”

Mr. Menendez had resisted calls to step down before his trial, but he could now face a rare expulsion vote by his Senate colleagues if he does not leave voluntarily. If the seat is vacated, Gov. Philip D. Murphy of New Jersey would be able to name a replacement to fill out his term.