VINEYARD HAVEN, Mass. — In yet another twist in their complex and heavily scrutinized relationship, Hillary Rodham Clinton and President Barack Obama did their best to shrug off their differences Wednesday as they gathered together on Martha’s Vineyard following a foreign policy split.

Obama’s spokesman said the White House “is looking onwards and upwards,” while Clinton joked she was planning on hugging it off with her former boss at a birthday party for a mutual friend on the island getaway where Obama is vacationing.

“We have disagreements as any partners and friends, as we are, might very well have,” Clinton told reporters crowded into a bookstore signing of her memoir “Hard Choices.” ”But I’m proud that I served with him and for him, and I’m looking forward to seeing him tonight.”

Clinton, Obama and their spouses sat together later in the evening for a surf and turf dinner celebration for 150 people at the Farm Neck Golf Club. The White House said the Obamas were happy to have time with the Clintons, and noted that Obama and Clinton were among those who delivered 80th birthday toasts to guest of honor Ann Jordan, wife of Democratic adviser Vernon Jordan.

“The Obamas danced nearly every song. A good time was had by all,” White House spokesman Eric Schultz told reporters after Obama departed shortly after 10 p.m.

The media was not allowed in to see whether Clinton delivered her promised makeup hug after an interview with The Atlantic magazine in which she seemed to try to set herself apart from the unpopular Obama as she heads toward a possible 2016 White House bid.

“Great nations need organizing principles, and ‘don’t do stupid stuff’ is not an organizing principle,” she had said in the interview, referring to a version of the phrase Obama and his advisers have used privately to describe his approach to foreign policy.

Her critiques came at a particularly challenging time for Obama, with bombs falling on Iraq and disputes raging in Syria, the Mideast, Ukraine and elsewhere. A former top Obama adviser, David Axelrod, took to Twitter to write: “Just to clarify: ‘Don’t do stupid stuff’ means stuff like occupying Iraq in the first place, which was a tragically bad decision.” Clinton voted in favor of the Iraq War in 2002, while Obama voiced opposition.

It was Clinton’s biggest split with Obama since their 2008 presidential primary campaign when she questioned whether her younger Senate colleague was qualified to take a 3 a.m. phone call on a foreign policy emergency. Clinton took a more hawkish stance than Obama in that campaign, particularly on the Iraq War, but Obama put their bitter contest behind them by naming her his top diplomat.

Clinton loyally carried out Obama’s foreign policy agenda for four years as secretary of state, but described some objections she raised internally in her new book, which focused on her time in the administration. She expanded on those objections in her interview, saying Obama’s “failure” to fully support the rebels in Syria fueled the rise of Islamic State militants now the object of U.S. airstrikes in Iraq.

Reporters who crowded in front of a table set up for Clinton’s signing at the Bunch of Grapes bookstore asked her whether she disagreed with Obama’s Iraq policy.

“I’m excited about signing books,” she said, turning to a line of hundreds that snaked through the rainy streets near the ferry dock that brings summer visitors to the island. About 1,000 copies of the book were bought in advance, and the store was open only for those who had made the purchases.

Schultz declined to say whether the president was upset over her critique of his performance as he juggles several crises overseas, although he acknowledged “an honest policy difference” on the Syrian rebels. Schultz said Obama appreciated that Clinton called the president Tuesday to say she was not trying to attack him.

“They have a close and resilient relationship,” Schultz said.

Martha’s Vineyard native Dana Jacobs, a sophomore at Boston’s Northeastern University, said she was a supporter of Obama but a bigger fan of Clinton after reading in her book how she handled foreign policy challenges. She said Obama was dealt “a really difficult hand of cards.”

“I think something more dramatic would have been good, a little more change,” Jacobs said, as she left clutching a signed copy of the book in which Clinton described her world view.