"In the interests of the country, I think it's time to wrap it up," Pence said on NBC's "TODAY" following the release of three Americans held by North Korea.
"I would very respectfully encourage the special counsel and his team to bring their work to completion."
Mueller is investigating potential links between the Trump presidential campaign and the Kremlin, as well as matters that "may arise directly from the investigation."
The interview came days after porn star Stormy Daniels' lawyer, Michael Avenatti, alleged that more than $4 million from companies including AT&T, Novartis and Korea Aerospace Industries was paid to a company created by President Donald Trump's personal attorney, Michael Cohen.
Cohen's company, Essential Consultants, created in October 2016, was used to pay Daniels $130,000 as part of a nondisclosure agreement barring her from discussing an alleged sexual encounter she had with Trump.
AT&T and Novartis later confirmed they had made payments to the company, though their reasons for doing so varied. Cohen's lawyers pushed back on the report in a court filing Wednesday, pointing to what it said were "numerous inaccurate statements." Avenatti responded by saying that the inaccuracies in the report were relatively small and that his findings were "99.0% right."
Pressed on the reported payments made to Cohen's company, Pence said that's a "private matter" and "something I don't have any knowledge about."
While Pence has rarely commented on the special counsel, Trump has publicly decried the investigation as a "witch hunt."
The Associated Press contributed to this report.