"Senator McConnell appreciates the outpouring of support he’s receiving while he continues his recovery in the hospital," said a McConnell spokesperson.
"The Senator continues to improve, and is working closely with his staff on Kentucky and Senate matters while the Senate is out of session."
Senate Republican leaders are actively working to dispel rumors about the 84-year-old lawmaker's condition.
Senate Majority Leader John Thune and Senate Majority Whip John Barrasso both reported having phone conversations with McConnell.
"Their phone call lasted roughly 20 minutes.
They caught up about the latest news impacting Senate races, the Graham Platner scandal, and the recent Supreme Court ruling on coordinated spending limits," said Kate Noyes, spokeswoman for Barrasso.
The Republican leaders also coordinated on the upcoming legislative agenda for the summer session.
"They also discussed the Senate’s July work period, including the need to pass the NDAA and confirm President Trump’s nominee for Director of National Intelligence," continued Noyes.
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"Senator McConnell was fully engaged and is eager to get back to the Senate."