WASHINGTON — President Trump’s national security adviser said on Sunday that North Korea could dismantle all of its nuclear weapons, threatening missiles and biological weapons “in a year,” a far more aggressive schedule than the one Secretary of State Mike Pompeo outlined for Congress recently, reflecting a strain inside the administration over how to match promises with realism.

The statements by John R. Bolton, the national security adviser and historically a deep skeptic that North Korea will ever fully disarm, came as Mr. Pompeo prepares to make his third trip to North Korea late this week.

Mr. Pompeo will arrive in Pyongyang with a proposed schedule for disarmament that would begin with a declaration by North Korea of all its weapons, production facilities and missiles. The declaration will be the first real test of the North’s candor, amid increasing concern that it may be trying to conceal parts of its nuclear program. But Mr. Bolton, appearing on CBS’s “Face the Nation,” said Sunday that, nearly three weeks after the North Korean leader, Kim Jong-un, and President Trump met in Singapore, no such declaration has arrived.

Advisers to Mr. Pompeo, both outside the government and inside the C.I.A., which he used to direct, have cautioned him that North Korea will not give up its arsenal of 20 to 60 weapons until the last stages of any disarmament plan — if it gives them up at all. Many of the plans they have given him call for the North to halt production of nuclear fuel — at a moment that there are signs of increased production — but do not insist on dismantling weapons until Mr. Kim gains confidence that economic benefits are beginning to flow and that the United States and its allies will not seek to overthrow him.