(CNN) Senate Majority Leader Mitch McConnell is rejecting calls to keep his chamber in recess next week while the coronavirus epidemic is still on the rise across the country and in Washington in particular, as his top aides and the Capitol physician's office are in active discussions to prepare the body for a return to session during the public health crisis.

On a private conference call on Thursday afternoon, the Capitol's attending physician, Dr. Brian Monahan, detailed new procedures that Senate offices should take to limit the footprint in the chamber and keep aides who are feeling ill away from the Capitol. But Monahan indicated that the Capitol lacks the testing capacity to regularly test all senators, saying that tests would only be made available to those who are sick, according to two sources familiar with the call.

The 53-member Senate GOP Conference is still prepared to meet for lunch from Tuesday-Thursday when the Senate returns to session, but senators will be limited to three per table to reduce their risk of exposure to the virus, according to sources familiar with the call. The last time the Senate was in session: GOP Sen. Rand Paul was regularly attending party lunches before he learned he tested positive for the coronavirus

But the lunches are crucial for Senate Republicans because they are expected to debate how to approach the next package to stem the economic crisis, something that McConnell's chief of staff, Sharon Soderstrom, said would be a focus when the Senate reconvenes. The other agenda item, she said: renewing the expired Foreign Intelligence Surveillance Act, according to sources familiar with the call.

McConnell has made clear publicly and privately that he plans to push full steam ahead to confirm more of President Donald Trump's judicial nominees, prompting outcry from Democrats who say the Senate should only be reconvening if the focus was squarely on oversight of the coronavirus response and passing a new relief package.

"I think we can conduct our business safely," McConnell told Fox News in an interview Thursday. "We've got a whole lot of other people showing up for work during the pandemic. It's time for the Senate to do that as well. We have many confirmations, for example. The Senate is in the personnel business. The House is not."

What's caused particular concern is that many senators fall into the high-risk category for age and pre-existing conditions that make them vulnerable to coronavirus. Two-thirds are over age 60. That includes six senators over age 80, 22 over 70, and 39 over 60.

Others have pre-existing conditions. The 78-year-old McConnell, a polio survivor as a child, had heart surgery in 2003. Arkansas Republican John Boozman had heart surgery in 2014. Paul of Kentucky was injured during a recent attack by a neighbor and is missing part of a lung . Democratic Sen. Mazie Hirono of Hawaii and Sen. Michael Bennet of Colorado have each battled cancer.

Asked on the GOP conference call if older senators could get tested regularly, Monahan was not able to commit to that, according to the sources familiar with the call.

Eighty-six-year-old Democratic Sen. Dianne Feinstein of California called on McConnell on Wednesday to reverse course saying Democratic leaders who run the House were smart to follow the guidance of Monahan who urged them not to bring lawmakers back next week.

Asked if he had gotten different advice from Monahan about whether the Senate -- which has only 100 members compared to 435 in the House -- should return to work, McConnell would not directly answer other than to say, "we can modify our routines in ways that are smart and safe."

On a separate GOP conference call Thursday, McConnell didn't offer many details about the Senate's upcoming agenda or the procedures for carrying out business when the chamber returns next week, according to two people on the call.

McConnell told GOP senators that more guidance will come from the Capitol physician's office over the next day or so.

On the call with staff, Senate GOP aides made clear that hearings will only take place in two or three of the larger rooms in the Senate so members can be spread out.

A top aide on the Senate Rules Committee told GOP aides that the common spaces in the building and individual offices have been cleaned thoroughly -- and said that hand sanitizer and masks would be provided to offices.

Monahan said that Senate offices should minimize the number of staff in the building, create a process to screen visitors into their offices, employ more social distancing procedures and take a "greater interest" in the health of their employees. On that last point, he said that Senate aides who are coming to the Capitol should review a checklist of their symptoms before coming into the office. If they answered "yes" to any of the six questions, they should not come into work.

The Capitol itself will look different.

McConnell's chief urged aides to wear masks in the building and said her staff would be "leading by example" -- and would be wearing masks from the moment they get out of their cars in the morning.

When it comes time for the Senate to vote, there will be staggered arrivals for senators to limit the number of members on the floor. Monahan indicated that members should not gather and congregate in small groups on the floor, as they tend to do.

While McConnell's top aide told staffers that the current practices would be in place for at least two weeks, she indicated that the Senate schedule is expected to remain mostly the same: Senators returning for a Monday evening vote and then departing Thursday afternoon.

McConnell's spokesman declined to comment on the call.

Senate Minority Leader Chuck Schumer said on Thursday that he will "scrutinize" McConnell's safety guidelines for returning to session next week, which he said McConnell will release Friday.

Speaking to reporters on a conference call, Schumer said McConnell never consulted him about returning next week and said he will review the GOP leader's safety plans "very carefully" to make sure all senators and "workers are protected in every way." His comment came in response to a question pointing to a highly diverse workforce in Washington, DC -- nearly 50% African American -- many of whom work at the US Capitol in service jobs.

"We are going to scrutinize Leader McConnell's plan very carefully to see if it does provide the needed protections for the staff and the workers who are here," he said.

Schumer also reiterated Democrats' call for prioritizing oversight hearings on the administration handling of the coronavirus pandemic, which has left the country without widespread Covid-19 testing months into the crisis.

For her part, House Speaker Nancy Pelosi said Thursday that the House's current plan is to return the week after next to advance another coronavirus relief package.

"We're not coming back next week," Pelosi said during her weekly press conference. "Our plan is to come back the following week."

But she also said the House is "at the mercy of the virus" and the schedule will depend on guidance from the Capitol attending physician and the sergeant at arms.

Ahead of the Senate's return next week, former Treasury Secretary Hank Paulson talked to GOP senators during Thursday's private GOP conference call about the current economic crisis and compared it to the 2008 financial crisis. During the call, Paulson made the case for an aggressive Washington intervention into the economy -- even as many Republicans are eager to hit pause after nearly $3 trillion has been spent this spring alone.

Republican Sen. Mike Braun of Indiana told CNN that Paulson said that going "too much further into a lockdown" could further cripple the economy. "He said there's a window of opportunity to get the economy going," Braun said. "He said at this stage, we could avoid some of the things that happened in 2008-2009."

Braun said he asked Paulson about the skyrocketing deficit, and Paulson's message was that "we gotta get through this pickle first" and then deal with the serious structural deficit problems.

In addition to concerns over bringing the Senate back into session, Democrats are also troubled by the expectation the Senate will move soon to confirm a young District Court judge from Kentucky -- Justin Walker -- to a seat on the powerful US Court of Appeals for the DC circuit, often considered the second most powerful court in the country.

Feinstein, the top Democrat on the Senate Judiciary Committee, wrote this week to Chairman Lindsey Graham, a Republican from South Carolina, urging him to put off confirmation hearings and focus the committee's attention on battling coronavirus, such as keeping law enforcement and corrections employees safe.

This story has been updated with additional developments Thursday.

CORRECTION: This story has been updated to correctly reflect the health status of US senators who have fought cancer.