Mr Pence said in a Fox News interview that such a move would be a "great mistake" by the North Korean leader.
He also said there was "no question" that Mr Trump could walk away from the 12 June summit.
North Korea has threatened to pull out of the meeting after comments by US National Security Adviser John Bolton.
The country reacted furiously when Mr Bolton suggested it would follow a "Libya model" of denuclearisation.
N Korea threatens to cancel Trump summit
North Korea crisis in 300 words
Libya's former leader Muammar Gaddafi agreed with Western powers in 2003 to dismantle his programme in return for the lifting of sanctions. Eight years later he was killed at the hands of Western-backed rebels.
North Korea is also angry at current US-South Korea military drills and has halted talks with the South in response.
South Korean President Moon Jae-in plans to meet Mr Trump in Washington on Tuesday to discuss plans for the summit.
Only deal with US will save Kim - Trump
Could defectors affect North Korea talks?
Mr Pence said that Mr Trump would be willing to walk away from the planned Singapore meeting.
"I don't think President Trump is thinking about public relations, he's thinking about peace," the vice-president said.
The New York Times reported on Sunday that the US president is asking aides and advisers whether he should continue to go forward with the summit.
Meanwhile, a group of journalists from the UK, US, Russia and China has flown in to North Korea from Beijing to cover the ceremony marking the dismantling of the country's nuclear test site later this week.
The exact date and timing for the ceremony at the Punggye-ri site has yet to be announced.
Journey to North Korea's nuclear heart
The Western, Russian and Chinese journalists are making their way to North Korea's remote Punggye-ri nuclear test site to witness its dismantling.
They have flown into the city of Wonsan. Tom Cheshire from the UK's Sky News says their onward journey will take in dirt roads and a two-hour hike to an observation area.
The site, in the country's mountainous north-east, is thought to be the North's main nuclear facility and the only active nuclear testing site in the world.
Testing has taken place in a system of tunnels dug below nearby Mount Mantap.
North Korea presented its offer to scrap the site as a concession during diplomatic rapprochement with South Korea and the US.
But scientists believe the site partially collapsed after the latest test last September and may be unusable.
Only media are attending the ceremony, not expert monitors, and the invitation to South Korean reporters was withdrawn amid the ongoing spat over the military drills.
He also said there was "no question" that Mr Trump could walk away from the 12 June summit.
North Korea has threatened to pull out of the meeting after comments by US National Security Adviser John Bolton.
The country reacted furiously when Mr Bolton suggested it would follow a "Libya model" of denuclearisation.
N Korea threatens to cancel Trump summit
North Korea crisis in 300 words
Libya's former leader Muammar Gaddafi agreed with Western powers in 2003 to dismantle his programme in return for the lifting of sanctions. Eight years later he was killed at the hands of Western-backed rebels.
North Korea is also angry at current US-South Korea military drills and has halted talks with the South in response.
South Korean President Moon Jae-in plans to meet Mr Trump in Washington on Tuesday to discuss plans for the summit.
Only deal with US will save Kim - Trump
Could defectors affect North Korea talks?
Mr Pence said that Mr Trump would be willing to walk away from the planned Singapore meeting.
"I don't think President Trump is thinking about public relations, he's thinking about peace," the vice-president said.
The New York Times reported on Sunday that the US president is asking aides and advisers whether he should continue to go forward with the summit.
Meanwhile, a group of journalists from the UK, US, Russia and China has flown in to North Korea from Beijing to cover the ceremony marking the dismantling of the country's nuclear test site later this week.
The exact date and timing for the ceremony at the Punggye-ri site has yet to be announced.
Journey to North Korea's nuclear heart
The Western, Russian and Chinese journalists are making their way to North Korea's remote Punggye-ri nuclear test site to witness its dismantling.
They have flown into the city of Wonsan. Tom Cheshire from the UK's Sky News says their onward journey will take in dirt roads and a two-hour hike to an observation area.
The site, in the country's mountainous north-east, is thought to be the North's main nuclear facility and the only active nuclear testing site in the world.
Testing has taken place in a system of tunnels dug below nearby Mount Mantap.
North Korea presented its offer to scrap the site as a concession during diplomatic rapprochement with South Korea and the US.
But scientists believe the site partially collapsed after the latest test last September and may be unusable.
Only media are attending the ceremony, not expert monitors, and the invitation to South Korean reporters was withdrawn amid the ongoing spat over the military drills.