Former Presidents George W. Bush and Bill Clinton poked fun about ageing and traded stories about their grandchildren during a public appearance together on Thursday night.

Although their family members -- Jeb Bush and Hillary Clinton -- are campaigning in a hotly contested race to win the White House, there was little to no signs of tension between the former commanders in chief as they shared a stage together for the graduation of the Presidential Leadership Scholars program, a new partnership between their presidential centers.

"Clinton and I are getting a little long in the tooth these days," joked Bush, 69, about the 42nd POTUS while speaking in Dallas, reports NBC News.

"This is the one month a year when he's older than me. So speak for yourself," Clinton, 68, quipped in response.

In addition to teasing one another about getting older, the leaders talked about the joys of being a grandparent.

"When you become a grandfather you fall in love," Clinton said.

Clinton also revealed that he and his wife have been babysitting their 9½-month-old granddaughter, Charlotte, for three days.

"She wasn't a candidate for anything, she was grandmother of the year," he said about the former first lady, adding that Charlotte pointed to him when Clinton said, "Oh, there's your granddad."

In response, Bush said, "Last night, my granddaughter spoke to me in Mandarin."

The two men, who have reportedly become close friends after leaving the White House, spoke briefly about their loved ones' presidential campaigns. Bush also confirmed that he does not plan to step in during his brother's campaign.

"I know Jeb, and I'm confident Secretary Hillary will elevate the discourse," he said, reports Politico. "I can't attest to their surrogates. I can attest to this surrogate -- I'm not going to be a surrogate."

Clinton, meanwhile, said the focus of the 2016 candidates should be on convincing voters that they will be best president to create "shared prosperity."

"I hope we clarify for the American people that this is a big bunch of choices, they're not simple, but we can do it," Clinton said. "That's all I really care about, besides I know who I'd like to win. The more important thing for America is we know what the heck we're deciding on and we make a good decision."

Watch the full graduation ceremony of the inaugural class of the Presidential Leadership Scholars program below.