The Senate’s top two Republicans said on Tuesday that they recently spoke with Senator Mitch McConnell of Kentucky, offering brief updates on the status of the 84-year-old senator who has been hospitalized since June 14 as questions mount over his condition.

Senator John Thune of South Dakota, the majority leader, said in a statement that he spoke with Mr. McConnell by phone on Monday in a “lengthy and substantive conversation.” Senator John Barrasso of Wyoming, the No. 2 Senate Republican, said he spoke with Mr. McConnell on the phone for “roughly 20 minutes” on Tuesday in a discussion that spanned “the Graham Platner scandal and the recent Supreme Court ruling on coordinated spending limits.”

Scott Jennings, a former adviser to Mr. McConnell and a CNN analyst, also said he spoke with the senator on Tuesday morning for “just shy of 20 minutes.”

“He’s still recovering in the hospital,” Mr. Jennings wrote on social media.

The three men did not elaborate on Mr. McConnell’s condition or prognosis. Mr. McConnell’s office said in a statement on Tuesday that “the senator continues to improve and is working closely with his staff on Kentucky and Senate matters while the Senate is out of session.”

The statements came amid an outpouring of rumor and speculation about Mr. McConnell’s condition. His office has not released any details about his condition, what prompted his hospitalization, the treatment he is receiving or his expected timeline for recovery.

Recordings of emergency dispatcher radio communications logged between 8:36 a.m. and 8:43 a.m. the day he was hospitalized indicate that dispatchers initially called for medics to respond to a report of an unconscious individual at Mr. McConnell’s Washington address. Six minutes later, a worker with the city’s Fire and Emergency Medical Services Department responded, asking that his supervisor be informed of “CPR in progress.”

Mr. McConnell’s office has declined to comment on the recordings, even after they were reported on by multiple news outlets.