(CNN) President Barack Obama met in January 2017 with then-FBI Director James Comey and other top national security officials to discuss sharing information related to Russia with the incoming Trump administration, where Obama stated that the Trump-Russia investigation should be handled "by the book," according to an email made public Monday and a source familiar with the matter.

The previously undisclosed meeting was memorialized in an email written by then-National Security Adviser Susan Rice on Donald Trump's Inauguration Day. A person familiar with the January 5, 2017, meeting said the Obama administration wanted to know whether the FBI and others in the intelligence community believed there was a national security reason to limit conversations with the Trump transition about Russia because some on the incoming President's team could be compromised.

The email was disclosed by Senate Judiciary Chairman Chuck Grassley and Sen. Lindsey Graham, who sent a letter Monday to Rice asking why she had sent the email to herself on the day of Trump's inauguration about an Oval Office meeting on Russian election interference. The meeting included Obama, Vice President Joe Biden, Comey and former Deputy Attorney General Sally Yates.

"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,' " Rice wrote. "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."

In a statement, Grassley and Graham said, "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.' "

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