Sen. Jeanne Shaheen Cynthia (Jeanne) Jeanne ShaheenSenate Democrats introduce bill to sanction Russians over Taliban bounties Trump-backed candidate wins NH GOP Senate primary to take on Shaheen Democratic senator urges Trump to respond to Russian aggression MORE (D-N.H.) on Sunday warned of "widespread" phishing attacks against Senate offices and political parties across the country, revealing that her office had already notified authorities of one suspicious experience.

"There has been one situation that we have turned over to authorities to look into," Shaheen, a member of the Senate Foreign Relations Committee, said on CBS's "Face the Nation."

"We're hearing that this is widespread with political parties across the country, as well as with members of the Senate."

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Shaheen's comments came after Sen. Claire McCaskill Claire Conner McCaskillMomentum growing among Republicans for Supreme Court vote before Election Day Democratic-linked group runs ads in Kansas GOP Senate primary Trump mocked for low attendance at rally MORE (D-Mo.) confirmed last week that her Senate computer system had been targeted unsuccessfully by Russian hackers. The attempt was detected by Microsoft.

Tom Burt, Microsoft's corporate vice president for customer security and trust, said last week during a session at the Aspen Security Forum that the company had uncovered three attempts by Russians to hack into the online accounts of staffers on three congressional campaigns.

The attempted cyberattacks are indicative of what U.S. national security and intelligence officials have warned is a new attempt by Moscow to interfere in the 2018 midterm elections.

Phishing attacks involve sending emails that appear to be from trusted sources, but in truth, trick the recipients into divulging personal information, such as online passwords.

President Trump Donald John TrumpSteele Dossier sub-source was subject of FBI counterintelligence probe Pelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' Trump 'no longer angry' at Romney because of Supreme Court stance MORE has repeatedly wavered on the U.S. intelligence community's assessment that Moscow meddled in the 2016 presidential election. During a joint news conference with Russian President Vladimir Putin earlier this month, he appeared to cast doubt on that conclusion, saying he saw no reason why Russia would interfere in U.S. affairs.

He later reversed course after coming under pressure from Republicans and political allies, saying that he misspoke. Still, he has faced criticism from lawmakers on both sides of the aisle who have expressed concern that he has not been aggressive enough in addressing election interference.

"This is a very big issue and it's something that we need to address in a bipartisan way," Shaheen said. "It affects both Republicans and Democrats. It's about the security of our political process and our government functions and we need to work together to address it."