Libertarian presidential candidate Gary Johnson Gary Earl JohnsonWhat the numbers say about Trump's chances at reelection Presidential race tightens in Minnesota as Trump plows resources into state The Hill's Campaign Report: Biden condemns violence, blames Trump for fomenting it l Bitter Mass. primaries reach the end l Super PAC spending set to explode MORE is reaching out to Republicans fleeing Donald Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE’s candidacy in the wake of backlash over the GOP nominee’s past sexually explicit comments.

“It’s time to vote your conscience,” Johnson said in a statement Saturday.

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“Our nation and our challenges are much greater than the character or behavior of one man. Join us, and we pledge to present voters with a real alternative to what has become an embarrassing side show."

The Libertarian ticket is comprised of two former Republican governors hailing from blue states – Johnson served as governor of New Mexico and his running mate Bill Weld served as governor of Massachusetts.

Earlier in the cycle, the candidates had some success appealing to younger voters and left-leaning independents who were not thrilled by the prospect of a Hillary Clinton Hillary Diane Rodham ClintonButtigieg stands in as Pence for Harris's debate practice Senate GOP sees early Supreme Court vote as political booster shot Poll: 51 percent of voters want to abolish the electoral college MORE presidency.

But Clinton has shored up much of that support in the wake of a strong first debate performance and several high-profile gaffes by Johnson in recent weeks.

Now, the Libertarian ticket is targeting Republicans who are fleeing from Trump in the wake of his latest scandal, which erupted Friday when leaked video from 2005 showed Trump commenting on women in sexually explicit terms.

“Character and trust are important,” Johnson said. “It shouldn’t matter whether a microphone is turned on or not. The conversation we have all now heard isn’t any more appropriate in a locker room than it is on national TV. America deserves better. Women certainly deserve better. And Republicans deserve better.”

“We speak often of reaching across party lines if elected to get things done for America," he continued. “Today, we would like to reach across party lines to invite our Republican friends to join our campaign. There is a presidential ticket with two candidates who served honorably and effectively as Republican Governors, and we are it.”

Some Republicans have been turned off by Johnson’s more liberal positions on social issues – he supports legalizing marijuana and abortion rights for women – as well as his anti-interventionist foreign policy views.

Some in the party, such as 2012 GOP nominee Mitt Romney, don’t view Johnson as a serious candidate.

Romney, who served as governor of Massachusetts after Johnson's running mate, said earlier this year that if Weld was at the top of the ticket he’d consider voting Libertarian.

Johnson has said that he and Weld are running as co-presidents and would share equal responsibilities in the White House.