Nearly half of Americans believe President Trump likely committed a crime related to Russian interference in the 2016 presidential election, according to a new poll published Thursday.

Of the 49% of Americans that think Trump likely acted illegally, 30% hold the belief on suspicion alone while 19% think there's already solid evidence to back it up, according to the Washington Post-ABC News poll.

The poll also found that more than half of Americans approve of the job Russia special counsel Robert Mueller is doing, while just over a quarter of Americans disapprove.

The survey of 714 Americans, conducted Oct. 30-Nov. 1, comes on the heels of Mueller's team filing the first criminal charges in its investigation and confirming publicly for the first time that someone in Trump's campaign sought an allegiance with Russians to gather “dirt” on his political rival.

The charges unsealed Monday included grand jury indictments of former Trump campaign chairman Paul Manafort and his associate Rick Gates on charges that they secretly worked on behalf of pro-Russian factions in Ukraine, then laundered millions of dollars in profits through foreign bank accounts.

More:Who's who: Key players in the investigation into Russian interference in the 2016 election

Also announced Monday: former adviser to Trump's campaign George Papadopoulos pleaded guilty to a charge that he lied to FBI agents about his contacts with a professor he believed "had substantial connections to Russian government officials" during the campaign. The professor offered him "dirt" — in the form of thousands of emails — on Trump’s election opponent, Hillary Clinton.

When asked about the charges brought against Manafort, almost 70% of Americans said they approved, according to the poll. More than half think those charges — as well as the cases against Gates and Papadopoulos — signal more widespread wrongdoing in the Trump campaign.

More:Mueller's bombshell: Special counsel charges Manafort, Gates and reveals aide's Russia contacts

More:Analysis: After Mueller's first charges, the White House braces for the next ones

Trump has long been critical of Mueller's probe, calling it a "hoax" and "witch hunt."

On Monday, Trump distanced himself from the investigation, denying any allegations of collusion and saying that the charges against Manafort stem from actions from "years ago" and that Papadopoulos was a "young, low level volunteer."

According to Thursday's poll, 51% of Americans think Trump is not cooperating with Muller's investigation.

Contributing: Kevin Johnson and Brad Heath

Follow Ryan Miller on Twitter @RyanW_Miller