"Trump and Kim have committed to denuclearisation of the entire Korean Peninsula".
Trump described his meeting with Kim as "an interesting and very positive experience" and said North Korea "has great potential for the future".
But he added: "Major disarmament".
"We hope that the outcomes of the US-DPRK Summit will be implemented, thus paving the way for lasting peace and stability in the Korean Peninsula", said the MEA.
Trump returned to Washington, declaring on Twitter "There is no longer a Nuclear Threat from North Korea", even though the agreement he signed with Kim does not spell out how Pyongyang will dismantle its nuclear weapons program.
Even as Pompeo staunchly defended the summit results, he was less exuberant than Trump, who tweeted on his return to the US on Monday morning: "Just landed - a long trip, but everybody can now feel much safer than the day I took office".
The credibility of that claim is in doubt. "I got them after we had signed the agreement".
Media captionTrump Kim summit: Win-win, or a Kim win? Moon held talks with Kim in April at which Kim agreed to work toward "complete denuclearization". He met Kim again in May when Trump said he was withdrawing from the planned summit with Kim - a decision Trump quickly reversed.
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The move - long demanded by Pyongyang - has been seen as a major concession to North Korea and appeared to take U.S. allies in the region by surprise.
US President Donald Trump (R) gestures as he meets with North Korea's leader Kim Jong Un (L) at the start of their historic US-North Korea summit, at the Capella Hotel on Sentosa island in Singapore on June 12, 2018.
What does the deal lack?
Vice President Pence on Tuesday afternoon told House and Senate Republican lawmakers that semiannual war games would cease - as long as North Korea follows through on efforts to denuclearize.
"While I am glad the president and Kim Jong Un were able to meet, it is hard to determine what of concrete nature has occurred", Corker said in a statement.
How has the deal been received?
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.
At the heart of negotiations was the "complete, verifiable and irreversible denuclearization" of the Korean peninsula in exchange for "security guarantees" for the North's mercurial leader, Kim Jong Un.
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".
But, in an oblique reference to Pakistan, a statement by the ministry of external affairs (MEA) said New Delhi's concerns about Pyongyang's nuclear proliferation linkages with India's neighbourhood should be addressed.