The North Koreans have increasingly called for sanctions relief, while the USA has insisted that denuclearization comes first.
Any testing of new weapons is likely to raise tensions with Washington, which has said there will be no easing in worldwide sanctions until North Korea takes more concrete steps to abandon its nuclear weapons or long-range missiles.
A US think tank said on Monday it had identified at least 13 of an estimated 20 active, undeclared missile bases inside North Korea, underscoring the challenge for American negotiators hoping to persuade Kim to give up his weapons programs.
US Secretary of State Mike Pompeo had been due to meet North Korea's Kim Yong Chol, a senior aide to Kim Jong Un, in NY earlier this month, but it was postponed to a later date.
Diplomacy has stalled since the June summit between Trump and Kim in Singapore, with Washington pushing for more action on nuclear disarmament and the North insisting the USA first approve a peace declaration formally ending the 1950-53 Korean War.
A meeting between a top North Korean official and secretary of state Mike Pompeo was abruptly cancelled last week.
Pence also said that Trump will push for a concrete plan outlining Pyongyang's moves to end its arms programmes.
Pence made the comments after meeting with South Korean President Moon Jae-in on the sidelines of the ASEAN summit in Singapore.
Moon said that the North's leader is expected to visit Seoul in the near future and a second U.S.
Briefing journalists on the Pence meeting, foreign secretary Vijay Gokhale said, "He (Modi) did point out that the mainstreaming of people involved in the Mumbai attacks + in a political process which has taken place in the recent elections in Pakistan should be a matter of serious concern not just to the two countries - India and the United States - but to the worldwide community".
North Korea's state media said on Friday that leader Kim Jong Un had inspected a site testing a "high-tech tactical weapon", South Korean Yonhap news service reported, the first mention by state media of a new development in weapons in months.
"Until we have a plan that is implemented to achieve complete, verifiable, irreversible, denuclearization, we're going to keep the pressure on", he said. Trump and Kim are both interested in another summit, but it's unclear when it might happen.
NBC contrasted Pence's alleged indifference to a full inventory of North Korean weapons with the Center for Strategic and International Studies report released this week about continued maintenance performed at North Korean missile bases, quoting report author Victor Cha's admonition that "we can't negotiate over things they don't admit having". He also said that a lot of progress has been made, but there still remains much work to do ahead.
Li also urged Asean members to work together to counter United States trade policies and complete negotiations on the Regional Comprehensive Economic Partnership (RCEP) - a free-trade deal between the 10 members of Asean and six other Asia-Pacific nations.
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