Attorney General Loretta Lynch and former President Bill Clinton met privately as they crossed paths at a Phoenix airport earlier this week — a meeting that took place as the FBI continues its investigation into likely Democratic presidential nominee Hillary Clinton’s use of a private email server as secretary of state.

“I did see President Clinton at the Phoenix airport as I was leaving, and he spoke to myself and my husband on the plane,” Ms. Lynch told reporters. “Our conversation was a great deal about his grandchildren. It was primarily social and about our travels. He mentioned the golf he played in Phoenix, and he mentioned travels he’d had in West Virginia.”

“He did come over and say hello and speak to my husband and myself and talk about his grandchildren and his travels and things like that,” she said.

“So that was the extent of that, and no discussions were held [on] any cases or anything of that. And he didn’t raise anything about that, either,” Ms. Lynch said.

The meeting came as the FBI continues to investigate Mrs. Clinton’s use of a private email server during her time as the nation’s top diplomat.

Two top Senate Democrats defended Ms. Lynch’s honor on Thursday as reports of the meeting came to light.

“I can’t control who meets with whom. All I can say is Loretta Lynch is one of the most outstanding human beings I’ve ever known,” Senate Minority Leader Harry Reid told reporters.

“Her ethics is above reproach,” said Mr. Reid, Nevada Democrat. “No one could ever question her strong feelings about the rule of law. And her ethics, I repeat, are the best.”

“She’s an honorable person — we know that,” said Sen. Charles E. Schumer, New York Democrat. “Our Republican colleagues have said it.”

“She has said nothing was discussed related to the investigation, so you have two choices: to say this didn’t matter, or she’s lying,” Mr. Schumer said. “I think it didn’t matter. I don’t think she’s lying.”

But Sen. Chris Coons, who is also supporting Mrs. Clinton for president, said Thursday that the meeting “doesn’t send the right signal.”

“I am impressed with Attorney General Lynch — the work that she’s done in combating violent crime and in leading the Department of Justice,” Mr. Coons, Delaware Democrat, said on CNN’s “New Day.” “She has generally shown excellent judgment and strong leadership of the department, and I’m convinced that she is an independent attorney general.”

“But I do think that this meeting sends the wrong signal. … I think she should have steered clear, even of a brief, casual social meeting with the former president,” he said.

“I think she should have said, ‘Look, I recognize you have a long record of leadership on fighting crime, but this is not the time for us to have that conversation. After the election’s over, I’d welcome your advice and input,’ ” Mr. Coons said.

When President Obama endorsed Mrs. Clinton for president earlier this month, the White House insisted the move would not affect the Justice Department’s investigation.

The meeting also came shortly before the Tuesday release of the House Select Committee on Benghazi’s report on the Sept. 11, 2012, terrorist attack in Libya that claimed the lives of four Americans. Mrs. Clinton, Mr. Clinton’s wife, was secretary of state at the time of the attack.