Ex-national security adviser Susan Rice sent an “unusual email” to herself the day President Trump was sworn in to office documenting former President Barack Obama's guidance at a high-level meeting about how law enforcement should investigate Russian interference in the 2016 presidential race, two Republican senators said Monday.

According to Senate Judiciary Committee Chairman Chuck Grassley and Sen. Lindsey Graham, the partially unclassified email was sent by Rice on Jan. 20, 2017 -- and appears to document a Jan. 5 meeting that included Obama, then-FBI Director James Comey, then-Deputy Attorney General Sally Yates, then-Vice President Joe Biden and Rice.

In the email, Obama's national security adviser wrote: “President Obama began the conversation by stressing his continued commitment to ensuring that every aspect of this issue is handled by the Intelligence and law enforcement communities ‘by the book.’ The president stressed that he is not asking about, initiating or instructing anything from a law enforcement perspective. He reiterated that our law enforcement team needs to proceed as it normally would by the book.”

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The email also appears to reflect Obama's guidance on sharing sensitive information with both the Russians and the incoming administration.

Rice wrote that Obama said "he wants to be sure that, as we engage with the incoming team, we are mindful to ascertain if there is any reason that we cannot share information fully as it relates to Russia."

She added, "The President asked Comey to inform him if anything changes in the next few weeks that should affect how we share classified information with the incoming team. Comey said he would."

Grassley, R-Iowa, and Graham, R-S.C., released the email Monday. They said they uncovered it as part of their oversight of the FBI and the Department of Justice, and claimed it raises new questions.

“It strikes us as odd that, among your activities in the final moments on the final day of the Obama administration, you would feel the need to send yourself such an unusual email purporting to document a conversation involving President Obama and his interactions with the FBI regarding the Trump/Russia investigation,” they wrote in a letter to Rice.

They added: “In addition, despite your claim that President Obama repeatedly told Mr. Comey to proceed ‘by the book,’ substantial questions have arisen about whether officials at the FBI, as well as at the Justice Department and the State Department, actually did proceed ‘by the book.’”

The origins of the Russia meddling probe have come under mounting scrutiny on Capitol Hill, where Republicans are looking at how an unverified anti-Trump dossier was used to seek a surveillance warrant against Trump associate Carter Page in late 2016.

The senators asked Rice to answer questions about the email by Feb. 22.

According to the released email, the Jan. 5 meeting followed a briefing by the intelligence community on Russian hacking during the 2016 election. Grassley and Graham said the meeting included a discussion of the now-infamous dossier.

But one source familiar with the meeting said it had nothing to do with Steele or the dossier. That person said it was solely focused on whether the intelligence community and the FBI needed to be careful about what Russia conversations they had with the Trump transition team.

Fox News' Mike Emanuel and Catherine Herridge contributed to this report.