Republican strategist: 'Stunned' by Trump's remarks, which put GOP in 'very difficult situation'

Trump needs to get over this episode as soon as possible so he can move on to talking about his agenda, former RNC press secretary Alex Conant said.

Republican strategist Alex Conant told CNBC on Tuesday he was "stunned" by President Donald Trump 's latest statements about the deadly white nationalist rally in Virginia.

During a Tuesday news conference on infrastructure, the president once again blamed both sides for the violence that erupted over the weekend. He defended the protest and contended that some of the individuals carrying torches did not have bad intentions.

Conant, a former press secretary for the Republican National Committee, said in an interview with " Closing Bell " that Trump "needs to get over this episode as soon as possible so he can move on to talking about his agenda."

Republicans "hate" having to answer questions on why Trump didn't condemn white supremacists more forcefully, because there's no good answer for that, he said.

"This is a big step backward," Conant said. "It puts Republicans in Congress and potential allies in corporate America in a very difficult situation."

Three CEOs had already resigned from the American Manufacturing Council this week since the weekend protest. After Trump's latest comments on Tuesday, AFL-CIO President Richard Trumka resigned from the council.

Meanwhile, reaction was swift from the nation's capital, with bipartisan criticism beginning immediately after the press conference.

Rep. Ileana Ros-Lehtinen, R-Fla., slammed the remarks on Twitter.

"Blaming "both sides" for #Charlottesville?! No," she wrote. "Back to relativism when dealing with KKK, Nazi sympathizers, white supremacists? Just no."

— CNBC's Jacob Pramuk contributed to this report.