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Senate Health Committee Chairman Lamar Alexander, R-Tenn., expressed his concerns on Tuesday about Congress coming back into session amid the ongoing coronavirus pandemic – saying the move "creates a highly efficient virus-spreading machine" if lawmakers aren't properly tested for the contagion.

The comments by Alexander come a day after the Senate met for the first time since mid-March after Majority Leader Mitch McConnell, R-Ky., called lawmakers back to the Capitol for a series of votes and confirmation hearings, and as McConnell and House Speaker Nancy Pelosi, D-Calif., declined the White House's offer to deploy rapid coronavirus testing capabilities to Capitol Hill.

“With the increasing number of diagnostic tests available, I expect attitudes to change quickly about accepting the president’s offer to test members of Congress for COVID-19, especially as the House of Representatives comes back to work. From a public health point of view, this is not mostly about protecting members of Congress. It is about protecting the people members might infect,” Alexander said. “Bringing 100 or 535 members from across the country to Washington, D.C.—a coronavirus hotspot—and then sending them home each weekend creates a highly efficient virus-spreading machine.”

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He added: “You would have to hire an army of public health workers to track and test all of those people that members of Congress might infect, not to mention their staffs and other Capitol workers. The country will soon be able to test two million Americans each week. This is enough to test 535 members of Congress each week before they go home to make sure they don’t spread the disease from a virus hotspot into every section of the country.”

Alexander’s criticism of Congress resuming work on Capitol Hill without taking the White House's offer of testing marks the first time one of McConnell’s fellow Republicans has made a dissenting comment about his move to bring lawmakers back to Washington.

Democrats, however, have been critical of McConnell’s move from the outset with Senate Minority Leader Chuck Schumer, D-N.Y., lashing out at McConnell on Monday for calling the upper chamber of Congress back into session despite warnings against doing so by the Capitol physician and worries that the virus could worsen in the Washington, D.C., area.

“The Republican leader has called the Senate back into session despite the District of Columbia appearing to be reaching a peak phase,” of the virus, Schumer said. “If we are going to make these fine people come into work in these conditions, the Senate should focus like a laser on COVID-19 … but the majority leader has scheduled no hearings on COVID-19.”

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Earlier, McConnell had defended his decision to return to the Senate amid the outbreak, calling his fellow lawmakers "essential workers" and roundly criticizing Democrats for obstructing the confirmation of judges and key government posts for months and forcing the Senate to hold roll calls and floor votes during the public health crisis.

“The deadly coronavirus does not take time off, so neither does the U.S. Senate,” McConnell said. “Qualified nominees who have been held up for too long are already more essential at this time.”

Sen. Dianne Feinstein, D-Calif., criticized McConnell’s classification of senators as “essential workers” and noted that she didn’t think the business the Senate is taking up this week was necessary.

“I looked at what I know is coming up and it’s not terribly essential. It just happens that this week isn’t terribly essential,” she said.

Fox News’ Chad Pergram and Jared Halpern contributed to this report.