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New White House chief of staff John Kelly recently called Attorney General Jeff Sessions to assure him his job was safe, Fox News has learned from a senior White House official and another source within the Trump administration.

Kelly called Sessions on Saturday to emphasize that the White House supported him and wanted him to continue leading the U.S. Department of Justice, the sources said.

The assurance comes despite tweets and comments about Sessions from President Donald Trump that came after the attorney general recused himself from the Russia collusion investigation.

Meanwhile, two members of the U.S. Senate Judiciary Committee are readying legislation intended to help special counsel Robert Mueller – who is leading the Russia collusion probe – keep his job as well.

Sen. Thom Tillis, R-N.C., and Sen. Chris Coons, D-Del., plan to introduce the legislation Thursday. It would allow any special counsel for the Justice Department challenge his or her removal in court, with a review by a three-judge panel within 14 days of the challenge.

The bill would be retroactive to May 17 -- the day Mueller was appointed by deputy Attorney General Rod Rosenstein to investigate Russian meddling in the 2016 election and possible ties to Donald Trump’s campaign.

“It is critical that special counsels have the independence and resources they need to lead investigations,” Tillis said in a statement. “A back-end judicial review process to prevent unmerited removals of special counsels not only helps to ensure their investigatory independence, but also reaffirms our nation’s system of check and balances.”

Mueller was appointed as special counsel in May following Trump’s firing of FBI Director James Comey.

Mueller, who was Comey’s predecessor as FBI director, has assembled a team of prosecutors and lawyers with experience in financial fraud, national security and organized crimes to investigate contacts between Moscow and the Trump campaign.

Trump has been critical of Mueller since his appointment, and his legal team is looking into potential conflicts surrounding the team Mueller has hired, including the backgrounds of members and political contributions by some members to Hillary Clinton. He has also publicly warned Mueller that he would be out of bounds if he dug into the Trump family’s finances.

Mueller has strong support on Capitol Hill. Senators in both parties have expressed concern that Trump may try to fire Mueller and have warned him not to do so.

“Ensuring that the special counsel cannot be removed improperly is critical to the integrity of his investigation,” Coons said.

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FILE - In this Sept. 4, 2013, file photo, then-incoming FBI Director James Comey talks with outgoing FBI Director Robert Mueller before Comey was officially sworn in at the Justice Department in Washington. On May 17, 2017, the Justice Department said it is appointing Mueller as special counsel to oversee investigation into Russian interference in the 2016 presidential election. (AP Photo/Susan Walsh, File) (AP)

Sen. Lindsey Graham, R-S.C., another member of the Judiciary panel, said last week that he was working on a similar bill that would prevent the firing of a special counsel without judicial review. Graham said then that firing Mueller “would precipitate a firestorm that would be unprecedented in proportions.”

The Tillis and Coons bill would allow review after the special counsel had been dismissed. If the panel found there was no good cause for the counsel’s removal, the person would be immediately reinstated. The legislation would also codify existing Justice Department regulations that a special counsel can only be removed for misconduct, dereliction of duty, incapacity, conflict of interest or other good cause, such as a violation of departmental policies.

In addition, only the attorney general or the most senior Justice Department official in charge of the matter could fire the special counsel.

In the case of the current investigation, Rosenstein is charged with Mueller's fate because Sessions recused himself from all matters having to do with the Trump-Russia investigation.

Fox News’ Serafin Gomez and the Associated Press contributed reporting to this story.