President Trump and French President Emmanuel Macron shared an intense handshake at their first meeting on May 25. (The Washington Post)

BRUSSELS — If relationships were defined by how two people shake hands, then the one between the newly elected presidents of the United States and France is going to be rather fierce.

As President Trump met French President Emmanuel Macron for the first time, welcoming him to lunch Thursday at the residence here of the U.S. ambassador to Belgium, the two men shook hands for six long seconds. Their knuckles turned white, their jaws clenched and their faces tightened. Trump reached in first, but then he tried to release, twice, but Macron kept his grip until letting go.

The meeting was on Trump's turf, but Macron, 31 years his counterpart's junior, signaled with his tight hold that the American was not the only alpha in the room.

But handshakes alone do not define relationships, of course. Although many contentious issues divide the two presidents -- perhaps most urgently, climate change -- Trump and Macron represent two longtime close allies and showed considerable respect for one another.

Trump, who is loath to talk about electoral victories other than his own, complimented Macron on his landslide win earlier this month in France's presidential runoff against a far-right candidate.

"It is my great honor to be with the newly elected president of France, who ran an incredible campaign and had a tremendous victory," Trump said. "All over the world they're talking about it."

"Congratulations," Trump added. "Great job."

Trump said he wanted to discuss terrorism and other issues, while Macron said they had "an extremely large agenda to discuss: the fight against terrorism, the economy, climate and energy."

"I am very happy to be able to change many things together," Macron said.

The French president, along with his counterparts from across Europe, is hoping to persuade Trump during his time at international summits here in Brussels and Friday in Sicily to maintain the U.S. commitment the 2015 Paris climate agreement.

Trump is in the process of deciding whether to stick to the climate accord, which was negotiated under President Barack Obama, and his advisers have been debating the matter vigorously.

Trump vowed during his campaign that he would withdraw from the Paris agreement, but he now is open to remaining in it, and on a number of other issues he has been persuaded to break his campaign promises.

Secretary of State Rex Tillerson told reporters that Trump intends to hear feedback from his foreign counterparts during his time abroad before making a decision.

For Trump and Macron, both newcomers to international diplomacy, Thursday's meeting was an opportunity to get to know one another, and perhaps form a bond.

As Macron pulled up outside the ambassador's residence and stepped out of a black Mercedes sedan, Trump and his wife, Melania, warmly greeted the French president, who arrived for lunch without his wife, Brigitte.

The presidents were served a three-course meal: a starter of tomatoes and buffalo mozzarella, veal fillet with chateau potatoes and tri-colored vegetables, and a duo of Belgian chocolate mousse.

Trump and Macron cut starkly different profiles as they built winning movements in their respective countries. Trump, 70, was a celebrity businessman and political outsider who campaigned as a populist and nationalist. Macron, 39, was a relatively unknown government insider who campaigned on an embrace of globalism.

Their differences were clear in their choice of attire Thursday. Each wore dark suits, but Trump's tie was thick and royal blue, with a slight shine, while Macron's was skinny and navy. And while Macron wore a standard shirt with a single button on the cuff, Trump opted for French cuffs, with large, diamond cuff links.