U.S. Secretary of State Mike Pompeo said Wednesday he expects North Korea to take major steps toward denuclearization before the end of President Donald Trump's first term in January 2021.

"We're hopeful that we can achieve that in the next -- what is it -- two and a half years, something like that," the top U.S. diplomat told reporters in Seoul when asked how soon Washington wants to see North Korea move to dismantle its nuclear weapons program. "We're hopeful we can get it done. There's a lot of work left to do."

Pompeo made the remarks after Trump declared the nuclear threat from North Korea over upon his return to the United States following his summit with North Korean leader Kim Jong Un.

(Mike Pompeo)

"Just landed - a long trip, but everybody can now feel much safer than the day I took office," Trump tweeted early Wednesday. "There is no longer a Nuclear Threat from North Korea. Meeting with Kim Jong Un was an interesting and very positive experience. North Korea has great potential for the future!"

On Tuesday, the two leaders signed a joint document that includes Pyongyang's commitment to "complete denuclearization" and Washington's pledge to provide it with security guarantees.

Some question the effectiveness of the statement because it makes no reference to concrete measures nor to a timeframe for achieving denuclearization.

Trump has also come under increasing criticism for his post-summit vow to suspend joint military drills between the United States and South Korea -- drills the North has denounced as preparations for invasion.

Pompeo said Wednesday that Washington could resume the drills once denuclearization negotiations with Pyongyang hit a snag.

He said his boss "made it very clear that the condition precedent for the exercises not to proceed was a productive, good-faith negotiations being ongoing."

"And at the point it's concluded that they are not, the president's commitment to not have those joint exercises take place will no longer be in effect," he said.