The US hopes to see "major disarmament" by North Korea by the end of 2020, Secretary of State Mike Pompeo says.
His comments come a day after an unprecedented meeting between President Donald Trump and North Korean leader Kim Jong-un in Singapore.
In a statement North Korea agreed to work towards "complete denuclearisation of the Korean Peninsula".
But the document has been criticised for lacking details on when or how Pyongyang would give up its weapons.
Speaking in South Korea, where he discussed the outcome of the summit, Secretary Pompeo said there was still "a great deal of work to do" with North Korea.
But he added: "Major disarmament... We're hopeful that we can achieve that in the two and half years."
He said he was confident Pyongyang understood the need for verification that it was dismantling its nuclear programme.
When asked by reporters why this was not specified in the document signed in Singapore, he condemned their questions as "insulting" and "ridiculous".
His comments come after President Trump declared that North Korea was no longer a nuclear threat, insisting "everybody can now feel much safer".
The credibility of that claim is in doubt. That is because under the deal, the North retains its nuclear warheads, the missiles to launch them and has not agreed to any specific process to get rid of them.
Pyongyang has celebrated the summit as a great win for the country.
What was agreed at the summit?
The declaration signed at the end of the summit said the two countries would co-operate towards "new relations", while the US would provide "security guarantees" to North Korea.
Pyongyang in return "commits to work toward complete denuclearisation of the Korean peninsula".
At a news conference after the meeting, Mr Trump said he would lift sanctions against North Korea once "nukes are no longer a factor".
He also announced an unexpected end to US-South Korea military drills.
The move - long demanded by Pyongyang - has been seen as a major concession to North Korea and appeared to take US allies in the region by surprise.
After the summit, North Korea's state media said the two leaders had agreed that "step-by-step and simultaneous action" was needed to achieve denuclearisation of the Korean Peninsula.
American hardliners such as Mr Trump's national security adviser John Bolton have previously opposed such a phased approach, whereby the US takes reciprocal action.
What does the deal lack?
Most Western observers have said the deal includes no new commitments from North Korea nor details on how denuclearisation could be achieved or verified.
At his news conference, President Trump said it was difficult to ensure anything but that he trusted his instinct that Mr Kim would abide by his word.
Critics also expressed disappointment that Pyongyang's long record of human rights abuses was not addressed.
How has the deal been received?
Japan's Prime Minister Shinzo Abe spoke to Donald Trump after the summit, saying there was "great meaning in Chairman Kim's clearly confirming to President Trump the complete denuclearisation".
Tokyo also, however, cautioned that despite Pyongyang's pledge for denuclearisation no concrete steps had been taken and that Japan would not let down its guard.
Defence Minister Itsunori Onodera said Japan saw "US-South Korean joint exercises and the US military presence in South Korea as vital to security in East Asia".
Chinese Foreign Minister Wang Yi described the Singapore summit as an "equal dialogue" between the two sides, adding that "no-one will doubt the unique and important role played by China: a role which will continue".
Chinese state media described the summit as a "starting point" but said "no-one would expect the half-day summit to be able to iron out all differences and remove deep-seated mistrust between the two long-time foes".
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