The Senate Intelligence Committee will begin as soon as Tuesday privately interviewing 20 people in its ongoing investigation of Russian involvement in the 2016 election as well as potential ties to the Trump campaign, its leaders said.

Committee Chairman Richard Burr said that "if there's relevance" to those and other interviews that he and Vice-Chairman Mark Warner anticipate scheduling, "they will eventually be part of a public hearing".

The two leaders stood side by side to update reporters about their investigation in a rare joint news conference on Capitol Hill, called just as the House Intelligence Committee's investigation appeared to be grinding to a halt.

Burr and Warner refused to comment on the political discord that has stymied the House Intelligence Committee's investigation since its chairman, Congressman Devin Nunes, went to the White House grounds last week without telling his committee colleagues to meet with a secret source.

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He said he viewed documents that may show that President Donald Trump or members of his transition team were improperly identified in reports regarding surveillance of foreign targets.

Democrats have accused Nunes of coordinating with the White House to distract attention from the investigation into potential ties between the Trump team and Russian officials, and they called for him to recuse himself from the Russia investigation or step down.

"We're not asking the House to play any role in our investigation. We don't plan to play any role in their investigation," Burr said.

While much of the House Intelligence Committee's political infighting has taken place in public, the Senate so far has conducted the entirety of its Russia investigation behind closed doors - except for a public hearing in January with FBI Director James Comey, National Security Agency Director Mike Rogers, then-Director of National Intelligence James Clapper and then-CIA Director John Brennan.

But the main difference between the House and Senate processes lies in how united the two Senate leaders are.

"Over the last month we've seen some progress," Warner said. Later, with a hand on Burr's shoulder, he added: "I have confidence in Richard Burr that we together, with the members of our committee, are going to get to the bottom of this."