WASHINGTON — Senator John McCain said Thursday that he intended to block President Obama’s nomination of Gen. Martin E. Dempsey to another two-year term as chairman of the Joint Chiefs of Staff. Mr. McCain made his announcement after he and the general had a testy exchange over whether the Obama administration was doing enough to assist the Syrian rebels.

“I’m actually going to put a hold on General Dempsey until General Dempsey responds to legitimate questions,” Mr. McCain said just two days after he helped negotiate a deal to ease the Senate confirmation process for Mr. Obama’s nominees.

Asked whether he would place the hold only after the Armed Services Committee forwarded the nomination to a vote by the full Senate, Mr. McCain responded tersely, “Before, after and during.”

“I want to see him answer the question,” he added. A vote by 60 senators can overcome a hold.

The confirmation battle grew out of a debate over whether the United States military should be ordered to more aggressively support Syrian rebels to oust the government of President Bashar al-Assad, including combat action like establishing a no-fly zone. Mr. McCain, who has called for American military intervention in the Syrian civil war, traveled to Syria in late May to meet with the rebel forces. It was the first time that a United States senator had traveled to Syria to meet with the rebels since the conflict erupted two years ago.