WASHINGTON — The White House national security adviser on Sunday described President Donald Trump’s summit with North Korean leader Kim Jong Un as a success despite the lack of an agreement providing for the verifiable dismantling of the North’s nuclear sites.

John Bolton, in three television interviews, tried to make that case that Trump advanced America’s national security interests by rejecting a bad agreement while working to persuade Kim to take “the big deal that really could make a difference for North Korea.”

The U.S. and North Korea have offered contradictory accounts of why last week’s summit in Vietnam broke down, though both pointed to American sanctions as a sticking point.

Bolton said the leaders left on good terms and that Trump made an important point to North Korea and other countries that negotiate with him.

“He’s not desperate for a deal, not with North Korea, not with anybody if it’s contrary to American national interests,” Bolton said.

Bolton also sought to e..