Washington (CNN) Special counsel Robert Mueller's investigation into Russian interference in the 2016 presidential election is "close to being completed," acting Attorney General Matt Whitaker said Monday.

Whitaker told reporters he has been "fully briefed" on the investigation.

"I look forward to Director Mueller delivering the final report," Whitaker said.

Whitaker's announcement follows new bipartisan legislation filed Monday that would require Mueller to summarize his findings in a report to Congress and the public.

The Russia investigation, which began when Mueller was appointed in May 2017 , has showed signs of nearing its end. Some of the investigation's prosecutors moved to different jobs outside of Mueller's office and the office moved some of its cooperators like former national security adviser Michael Flynn toward sentencing.

The arrest of former Trump adviser Roger Stone, one of the last key campaign associates in President Donald Trump's orbit, on Friday was also a long anticipated move from Mueller.

Deputy Attorney General Rod Rosenstein also will be leaving soon after attorney general nominee William Barr's confirmation. Rosenstein previously signaled to other officials that he would leave when he was satisfied that Mueller's investigation was either complete or close enough to completion that it was protected from potential interference.

Barr's confirmation hearings began Jan. 15, meaning that a vote could occur in mid-February at the earliest. An official briefed on the discussions surrounding Rosenstein's planned departure told CNN that Rosenstein wants to ensure a smooth transition, which includes the Mueller investigation.

But Mueller has indicated that a grand jury's work on the probe could continue. The special counsel's federal grand jury, which began meeting in July 2017, was extended in January so it may continue to meet and vote on criminal indictments for up to six more months.

The investigation has consistently returned results -- the grand jury has indicted former Trump campaign chairman Paul Manafort and his deputy Rick Gates, their Russian business associate Konstantin Kilimnik, 12 Russian military intelligence officers, 13 Russians and three companies that allegedly manipulated social media to sway US voters.

Manafort and Gates have since pleaded guilty to reduced sets of charges, with Mueller alleging in December that Manafort had lied on five major counts since agreeing to cooperate with the special counsel's office as part of his plea agreement.

Flynn, former Trump attorney Michael Cohen and campaign adviser George Papadopoulos have also pleaded guilty to charges from the special counsel's office.

Some Democrats unnerved

Whitaker also rattled some Democrats when he said decisions made by Mueller's office are going to be reviewed by the Department of Justice.

"I am comfortable that the decisions that were made are going to be reviewed through the various means we have," Whitaker said.

Some congressional Democrats expressed concern over those comments in interviews with CNN Monday afternoon.

Sen. Chris Coons, a Delaware Democrat who's a member of the Senate Judiciary Committee, said that it's "chilling" to hear Whitaker's comments.

"I don't have full confidence that acting Attorney General Whitaker intends to respect the independence of the special counsel and simply support and sustain the decisions he's made and simply release the report in full," Coons added.

Sen. Dianne Feinstein of California, ranking Democrat on the Senate Judiciary Committee, said, "He should not be a censor; it should stand on what Mueller and his group found."

Sen. Richard Blumenthal, a Connecticut Democrat who's another member of that committee, downplayed Whitaker's comments, saying he takes anything the acting attorney general says with a "giant iceberg worth of salt."

House Intelligence Chairman Adam Schiff, a California Democrat, said he thinks that Whitaker, or anyone else in the Department of Justice, should not have a say in what's in Mueller's report.

"The special counsel should speak for the special counsel's investigation," he said.

Sen. Sheldon Whitehouse, Democrat of Rhode Island, had harsh words for Whitaker.

"I'm not thrilled he's been fully briefed because I don't think he's independent or reliable," Whitehouse said.

He added that he's "not convinced" the probe is nearly completed. He said he thinks Whitaker may simply be delivering "administration talking points."

This story has been updated.