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With just over a week to go before the November 3 election in which Democrat Joe Biden is challenging the Republican president, the White House cited Pence's status as an "essential worker" as justification for his travel despite exposure to his chief of staff, Marc Short, who tested positive on Saturday.
The United States on Friday registered 84,244 new coronavirus cases and 79,852 cases on Saturday, the nation's largest daily totals since the beginning of a pandemic that has killed about 225,000 Americans and left millions of people jobless.
While Pence was set to campaign in North Carolina later on Sunday, Trump addressed a rally at an airport in New Hampshire.
"We are coming around, we're rounding the turn, we have the vaccines, we have everything. Even without the vaccines, we're rounding the turn," Trump told a crowd of cheering supporters on Sunday, many not wearing protective masks or observing social-distancing recommendations.
"It's going to be over. And you know who got it? I did. Can you believe it?"
While numerous Covid-19 vaccines are being developed, none has been approved for use in the United States.
Multiple senior aides to Pence also tested positive for Covid-19, the White House chief of staff said.
It marked the latest coronavirus infections in the White House, which have included Trump, first lady Melania Trump, their son Barron and numerous aides and associates.
The new infections offered a reminder of the way Trump - who was hospitalized for three nights this month after contracting Covid-19 - and those around him have downplayed the advice of public health experts to wear masks and observe social distancing guidelines to stem transmission.
In addition to dominating the campaign policy debate - with Trump insisting the United States is "rounding the turn" on the crisis, while Biden has blasted the president's disjointed response - the pandemic has changed Americans' voting habits, with 58.7 million ballots already cast.
Trump was also due to campaign in Maine on Sunday. Biden has no campaign events scheduled for Sunday. While Biden holds a wide lead in national opinion polls, polls show closer contests in some of the battleground states that could decide the outcome.
White House Chief of Staff Mark Meadows told reporters that White House doctors have cleared Pence to travel after Short tested positive. Pence is scheduled to address rallies in Kinston, North Carolina, later on Sunday and in Hibbing, Minnesota, on Monday.
Devin O'Malley, a spokesman for the vice president, said late on Saturday that Pence and his wife tested negative.
Asked on CNN's State of the Union why Pence was not following US Centers for Disease Control and Prevention guidelines to quarantine for 14 days after such exposure, Meadows on Sunday cited the vice president's status as "essential personnel."
Meadows said Pence would continue to campaign and speak at rallies.
Biden's running mate, Senator Kamala Harris, took four days off the campaign trail earlier this month after her communications director tested positive forCovid-19.
Speaking in Detroit as she campaigned in the battleground state of Michigan, Harris criticized Pence for continuing to travel, saying, "He should be following the guidelines."
Trump has mocked Biden for wearing a protective mask.
'A FREE SOCIETY'
Asked why the Trump campaign is not requiring people attending rallies to wear masks, Meadows said the campaign offers masks to attendees but, "We live in a free society."
"We're not going to control the pandemic. We are going to control the fact that we get vaccines, therapeutics and other mitigation areas," Meadows added.
Former New Jersey Governor Chris Christie, who himself caughtCovid-19 and was hospitalized for a week after spending several days at the White House without wearing a mask, on Sunday said he was "surprised" Pence would continue campaigning.
"Everybody's gotta put the health of the people they're going to be in touch with first," Christie told ABC's This Week programme.
Infectious diseases expert Dr Sandra Nelson of Harvard Medical School and Massachusetts General Hospital said it appeared that Pence would be at high risk for becoming infected and transmitting infection.
"With multiple members of his office testing positive this would be considered a work-based cluster. Anytime there is a cluster like this I would advise that the entire office transition to remote work for 14 days," Nelson said.