ALBANY - Gov. Eliot Spitzer, who gained national prominence relentlessly pursuing Wall Street wrongdoing, has been caught on a federal wiretap arranging to meet with a high-priced prostitute at a Washington hotel last month, according to a law enforcement official and a person briefed on the investigation.

The wiretap captured a man identified as Client 9 on a telephone call confirming plans to have a woman travel from New York to Washington, where he had reserved a hotel room, according to an affidavit filed in federal court in Manhattan. The person briefed on the case and the law enforcement official identified Mr. Spitzer as Client 9.

Mr. Spitzer, a first term Democrat, today made a brief public appearance during which he apologized for his behavior, and described it as a “private matter.” He did not address his political future.

“I have acted in a way that violates my obligation to my family and violates my or any sense of right or wrong,” said Mr. Spitzer, who appeared with his wife Silda at his Manhattan office. “I apologize first and most importantly to my family. I apologize to the public to whom I promised better.”