The 28-year-old, who won a team bronze medal at his first Olympics on Sunday night, told the Daily Mail that he would give the traditional gathering a miss in protest against what he sees as homophobia among the country's leadership.
The skater had also criticised Pence in an interview for supporting "homosexual conversion therapy".
Speaking at a press conference in Pyeongchang on Tuesday, Rippon said he stood by his recent criticism of Pence's position on LGBT rights.
"I have no problem about what I've said because I stand by it, but I think right now the Olympics are about Olympic competition," he said.
In January, Rippon condemned the decision to have Pence lead the 2018 US Olympic delegation to South Korea.
As Governor of Indiana, Pence signed the Religious Freedom Restoration Act, which allowed businesses to refuse service to gay and lesbian customers, citing religious freedom.
He later signed an amendment that prevented the law from being used to discriminate against LGBT customers.
After Rippon turned down the meeting with Pence, the latter responded by tweeting a message to the skater, urging him not to let "fake news distract you".
"I don't want my Olympic experience being about Mike Pence," he said.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)