John Kasich of Ohio is not expected to support the Republican nominee for president in the November election.
Kasich said on Tuesday that he would not vote for either Trump or his Cabinet nominees.
Trump won Ohio by 10 points in 2016.
Markell and other GOP officials have been under intense pressure to disavow Trump’s presidential campaign.
Trump is a former reality television star and real estate mogul.
Pence and the Indiana Republican Party did not immediately respond to requests for comment.
Trump has been endorsed by the National Rifle Association, which has said it supports Pence.
Pence has endorsed Trump in the past, but it was a campaign statement and not a position.
Trump has been accused of using racist, anti-Semitic and xenophobic slurs.
He also has repeatedly said that the election will be rigged.