Washington (CNN) Russian interference with American politics did not stop after the election, and prominent Republicans -- including House Speaker Paul Ryan and Sen. Marco Rubio -- have been targeted by coordinated social media attacks, cybersecurity experts told a Senate panel Thursday.

Rubio -- a former primary opponent of President Donald Trump -- announced at a Senate intelligence committee hearing on Russian meddling that during last year's election his former campaign staff was targeted by hackers twice.

Rubio said the attacks came from computers using IP addresses located in Russia -- once in July of last year, after he announced he would run again for the Senate and again, Wednesday morning. IP addresses do not necessarily confirm who conducted hacking, as it is relatively easy for hackers to mask their location.

"Former members of my presidential campaign team who had access to the internal information of my presidential campaign were targeted by IP addresses with an unknown location within Russia," Rubio said Thursday. "That effort was unsuccessful. I would also inform the committee within the last 24 hours, at 10:45 a.m. yesterday, a second attempt was made, again, against former members of my presidential campaign team who had access to our internal information -- again targeted from an IP address from an unknown location in Russia. And that effort was also unsuccessful."

Rubio's comment followed after one cybersecurity expert said Rubio himself had been the target of a Russian propaganda campaign designed to help Trump -- although the witness, former FBI agent and cybersecurity expert Clinton Watts, later said that all Republican opponents of Trump were targeted by Russians, not just Rubio.

"This past week we observed social media campaigns targeting speaker of the House Paul Ryan hoping to foment further unrest amongst US democratic institutions," Watts told senators.

The committee held its first public hearing on Russian meddling in the US election Thursday with calls for nonpartisanship, citing ongoing foreign interference that threatens "the heart of our democracy."

"The vice chairman and I realize that if we politicize this process, our efforts will likely fail," Committee Chairman Richard Burr, a North Carolina Republican, said in his opening remarks. "The public deserves to hear the truth about possible Russian involvement in our elections, how they came to be involved, how we may have failed to prevent that involvement, what actions were taken in response, if any, and what we plan to do to ensure the integrity of future free elections at the heart of our democracy."

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There was little chance that Thursday's hearing would be as explosive as the House intelligence committee's first public hearing last week, which started off with FBI Director James Comey confirming the FBI is investigating possible coordination between Trump campaign aides and Russian officials and included Trump himself fighting back during the hearing on Twitter.

Sen. Angus King, an independent from Maine who caucuses with Democrats, said on CNN's Erin Burnett "OutFront" Thursday evening that the work of the panel was multifaceted and could take awhile to find answers to all of the questions before it.

"I want to slow down a little bit," King said. "There's plenty of investigation yet to be done."

The differences between chambers was on full display as the Senate -- which gives the top Democrat on committees the title of vice chairman, unlike House's "ranking member" equivalent -- stressed bipartisan cooperation, the same day the leaders of the House committee were planning to meet and discuss the state of their troubled investigation.

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Thursday's hearing was not entirely without reference to political issues. Sen. Ron Wyden, an Oregon Democrat, made the case that the committee needed access to President Donald Trump's tax returns in order to investigate whether he'd been influenced by Russians.

"We need to follow the money," Wyden said. He also sought to understand the ties between Putin's administration, Russian oligarchs and Russian crime organizations, saying: "Russia's corruption problem, may be our corruption problem."

Watts responded that Wyden should "follow the trail of dead Russians," a clear reference to Putin critics who have turned up dead.

Senate investigators are hearing from experts on disinformation tactics -- tools used by Russian operatives in the US elections and elsewhere to disrupt elections.

"We are seeking to determine if there is an actual fire, but so far, there is a great, great deal of smoke," Sen. Mark Warner, the top Democrat and vice chairman of the committee, said in his opening remarks.

There is a brighter spotlight on the Senate committee to investigate Russian meddling in the election as its House counterpart has shattered along partisan lines, and even some Republicans calling on the Senate panel to lead Congress' probe.

Senate lawmakers also plan to interview former National Security Agency Director Keith Alexander and FireEye chief executive Kevin Mandia, a pair of cybersecurity experts, who are expected to answer questions about how Russian agents and an army of trolls utilized "fake news" throughout the 2016 election.

"There were upwards of 1,000 paid Internet trolls working out of a facility in Russia, in effect, taking over series of computers, which is then called a 'botnet,'" Warner, a Virginia Democrat, said Wednesday. "If you Googled 'election hacking' leading up to the election and immediately afterwards, you wouldn't get Fox or ABC, The New York Times, what you got is four out of the first five news stories that popped up were Russian propaganda."

Burr, meanwhile, said that he is keenly interested in Russia's attempts to influence European elections and whether Russian efforts in the US offer insights into their efforts to disrupt elections in Western democracies like France and Germany.

"We feel part of our responsibility is to educate the rest of the world about what's going on because it's now into character assassination of candidates," Burr said Wednesday.

Since that hearing, the House investigation has descended into chaos, but Senate investigators have stuck to a steady pace, largely ignoring their House colleagues.

Warner and Burr both said Wednesday they are taking a deliberative approach -- trying to learn as much as possible before calling in high-profile witnesses like former National Security Adviser Michael Flynn, former Trump campaign chairman Paul Manafort, former Trump foreign policy adviser Carter Page and former Trump adviser Roger Stone.

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Seven professional staff from their committee have been given special security clearances to review the documents and now have access to the same materials usually limited to Congress' "Gang of Eight" -- the Republican and Democratic leaders of the House and Senate and their respective intelligence committees.

And even though Manafort and Jared Kushner -- one of Trump's closest advisers who served as an intermediary for foreign policy and met with top Russian officials during the transition -- have offered to testify before Senate investigators, no date has been scheduled yet for them to come in.

Instead, Warner and Burr said that they have a list of 20 witnesses they plan to call in and have scheduled meetings with five of those witnesses so far. Both men declined to name those witnesses, but Burr implied it would be smart to expect Flynn to be on that list.

This story has been updated and will update to reflect breaking news.