The president made no reference to the wars that Canada and European allies have fought alongside the United States; the counterterrorism operations they have coordinated; the world trade system they have managed together; or the democratic political systems and respect for human rights that they share. If anything, experts said, this common history is a red flag to Mr. Trump.
“A consistent theme of the Trump administration has been to downgrade the value of allies and alliances,” said Richard N. Haass, the president of the Council on Foreign Relations. “To the contrary, they tend to be judged as military free-riders or economic rivals or both. That many are assertive, independent-minded liberals that regularly challenge the president only makes it worse.”
Officials in Japan and South Korea have been more reluctant than those in Europe or Canada to push back against Mr. Trump. But analysts in Asia said his comments in Singapore about withdrawing troops and canceling the joint military exercises left both countries rattled.
The widening fissures in America’s Pacific and Atlantic alliances, experts said, carry implications that go beyond bruised feelings or potential trade wars. In his single-minded focus on economic gain, sometimes poorly defined, critics say Mr. Trump risks undermining an international order built by the United States to bolster American security and values as well as prosperity.
In Europe, Russia could feel emboldened to bully its neighbors, confident that a divided West will do little to stop it. In Asia, the fraying of the America’s nuclear umbrella could encourage China to increase its military adventurism in the South China Sea.
The paradox of Mr. Trump’s transactional approach to statecraft is that the joint statement he signed with North Korea looks like the kind of deal he once derided. It does not commit the North to the complete, verifiable and irreversible denuclearization that his administration has long demanded. It does not address the North’s fleet of ballistic missiles. It does not even set a deadline for next steps.
“The bottom line,” said Daniel R. Russel, a former assistant secretary of state for East Asian affairs now at the Asia Society, “is that President Trump paid retail for a few warmed-over promises and appears to have given away both leverage and deterrence.”
Or, as Mr. Haass put it in a tweet on Tuesday, “The containment doctrine has given way to the condominium doctrine.”