WHITE HOUSE - U.S. President Donald Trump and German Chancellor Angela Merkel shook hands warmly at the end of a sometimes awkward "getting-to-know-you" session Friday at the White House that seemed to symbolize the difficulties ahead for the trans-Atlantic relationship.
Trump and Merkel, considered the two most powerful leaders in the Western world, appeared to get off to a rocky start in their first face-to-face meeting. They notably did not shake hands as they sat for photographers in the Oval Office after their opening conversation.
At a news conference later, however, following their two hours of talks, both leaders made more conciliatory statements.
"They were civil. It was workmanlike. They did not demonstrate any particular affinity, and one could sense there had been some significant differences of opinion in the meeting," said Charles Kupchan, senior fellow at the Council on Foreign Relations.
WATCH: Trump, Merkel Meet in Oval Office
Trump did not bring up the sharp criticisms of Merkel he issued when he was running for president last year, when he said the veteran chancellor's policy of welcoming immigrants was "ruining" her country and much of Europe. And Merkel was gentle in her comments about the immigration controversies in the United States since Trump took over the White House.
The problems of "migration, immigration, integration have to be worked on, obviously," Merkel said, adding: "But this has to be done while looking at the refugees as well, giving them opportunities to shape their own lives where they are. ... I think that's the right way of going about it. And this obviously is what we have an exchange of views about."
Trump, who once famously called NATO "obsolete," reaffirmed his support for the alliance, and Merkel said she was "gratified" by that. He did not, however, back down from previous criticism of allies who he says are not accepting their fair share of the defense burden.
WATCH: NATO Members 'Must Pay Fair Share,' Trump Says
Trump's NATO pledge welcomed
"I reiterated to Chancellor Merkel my strong support for NATO, as well as the need for our NATO allies to pay their fair share for the cost of defense," the U.S. president said. "Many nations owe vast sums of money from past years, and it is very unfair to the United States. These nations must pay what they owe."
Trump's NATO endorsement will be especially welcome to European ears, according to Jeffrey Rathke, deputy director of the Europe Program at the Center for Strategic and International Studies: "This is more than the president has ever said about NATO since being elected. So today was a bit more than that, and that will help reassure our allies of the U.S. commitment."
Trump also tried to ease concerns that he will move the United States toward protectionism, as he has been portrayed by many European media, but he repeated that he will seek better deals with trading partners.
"I don't believe in an isolationist policy," the president said. "But I also believe a policy of trade should be a fair policy. And the United States has been treated very, very unfairly by many countries over the years, and that's going to stop."
Watch: President Trump, German Chancellor Merkel Discuss Trade, NATO
Merkel seeks 'compromise ... good for both'
Merkel struck a conciliatory tone, while not yielding on key German interests. "We tried to talk about areas where we disagree, and find a compromise," she told reporters. "That is good for both, because we need to be fair."
The German chancellor emphasized the need for trade deals that benefit both sides, but she seemed to be emphasizing that any negotiation with the United States will be with the entire 28-member European Union, not with individual member states.
"I think it's only fair, and that's the purpose of concluding agreements: Both sides win," Merkel said. "And that's the sort of spirit in which we ought to be guided in negotiating any agreement between the United States and the EU. I hope we will come back to the table and talk about the agreement between EU and the U.S. again."
WATCH: Merkel Discusses US-EU Trade Agreement Talks
Veteran observers of U.S. trans-Atlantic relationships generally agreed that this first meeting of two very different leaders and experienced negotiators was a substantive start.
"At the beginning it was much more of, 'It's a good meeting, we are hopeful we can work together,' " said John Hughes, a former U.S. diplomat who is vice president of the Albright Stonebridge Group. "But, at the same time, it became evident in some of Merkel's responses [that] she doesn't see eye to eye with President Trump on everything, and she was going to be forceful in making her case on some of these issues, and not just bowing down to his demands."
Merkel told reporters that she and Trump had more discussions ahead on economic topics, during a late lunch at the White House, but she said she wanted to "project" her view about how Germany achieved its dominant role in Europe — that economic advancement has always been accomplished together with security and peace.
"The successes of Germans have always been those where Germany's gains are one side of the coin," Merkel said, "and the other side of the coin has been European unity and European integration. That is something of which I am deeply convinced."