Pence's comments follow a major speech in October in which he flagged a tougher approach by Washington towards Beijing, accusing China of "malign" efforts to undermine US President Donald Trump and reckless military actions in the South China Sea.
Earlier in the day, Prime Minister Modi participated in the ASEAN-India Breakfast Summit where he underlined the need for maritime cooperation and centrality of trade for the prosperity of the strategic Indo-Pacific region.
US Vice-President Mike Pence has delivered a veiled warning to Beijing over its rising strength in the Indo-Pacific, saying aggression should not be tolerated and offering reassurances of Washington's commitment to the region.
Giving details of the meeting, foreign secretary Vijay Gokhale told reporters that Mr Modi also hoped the USA would take into account the rich contribution of Indian-Americans in every sphere while deciding on the H-1B visa issue.
Trump is expected to speak more about enforcing sanctions when he meets Chinese President Xi Jinping at the G20 summit late this month and the unique role that China can play in ensuring the denuclearisation of the Korean peninsula, Pence said.
The Prime Minister is expected to speak to an expected audience of almost 40,000 people on the third day of the conference, November 14, Wednesday.
Pence and Moon were meeting on the sidelines of an Asia-Pacific summit hosted by Singapore.
The two leaders also had a brief discussion on trade-related matters.
Modi thanked Pence and reminded him that in one way or another all the traces and all the leads in the global terror attacks ultimately leads to a "single source and single place of origin", without naming any country or organisation.
The US said the North axed the talks because they weren't ready, and Trump insisted he was in "no rush".
Prime Minister Narendra Modi pointed out the "mainstreaming" of figures involved in the 26/11 Mumbai attacks in the recent elections in Pakistan, a clear reference to Lashkar chief Hafiz Saeed, during his interaction with U.S. vice-president Mike Pence in Singapore on Wednesday.
The two leaders also stressed need for maintaining a free and open Indo-Pacific while agreeing that there had been a substantial enhancement in the defence relationship and "our imports of equipment from the United States", Gokhale said.
"There was some good understanding of the areas of how we move forward in building cooperation on counter terrorism and both countries recognised that this is a challenge which we have to fight together and to fight along with the rest of the worldwide community", Gokhale said. He felt that India's contribution in ensuring this would be important. He also appreciated the cooperation between the U.S. and India on counter-terrorism. "We expressed our readiness to import more oil and gas from the United States as a way of expanding our trade", he said.
Pence thanked India in supporting the United States on its North Korean pressure campaign.