Chuck Hagel, the former Nebraska senator on President Obama’s short list for defense secretary, came under fire again on Thursday, this time for his record on gay rights and remarks he made 14 years ago about an openly gay nominee for a diplomatic post. Since Mr. Hagel’s name emerged as a candidate for the Pentagon last week, he has been sharply criticized for his record on Iran, Israel and militant groups like Hamas and Hezbollah, as well as comments he made about pro-Israel lobbying groups in Washington. The new round of criticism is focused on comments Mr. Hagel made in an interview about James C. Hormel, a San Francisco philanthropist nominated by President Bill Clinton to be ambassador to Luxembourg in 1997. Mr. Hagel, a Republican and a member of the Senate Foreign Relations Committee, was approached by his fellow Nebraskan in the Senate, Bob Kerrey, on behalf of Mr. Hormel, whose nomination was being held up by conservative Republicans. Mr. Hagel did not oppose the nomination when Mr. Hormel came before the panel. But he later spoke out against it, saying that an “openly, aggressively gay” man should not represent the United States.