Senator Mitch McConnell, the former Republican leader from Kentucky, who has been hospitalized for six weeks, said on Monday that he would not be returning to the Senate this week as lawmakers work toward their August recess.

In a statement from his office, Mr. McConnell, 84, also said that he would not be at this Saturday’s Fancy Farm, an annual state political picnic that he has attended for more than four decades and is a must for politicians in Kentucky.

“I’m still working hard to get back to my full schedule of work in the Senate and in Kentucky, keeping up with intense physical therapy per my doctors’ orders,” Mr. McConnell said in the statement. “Unfortunately, that means I won’t be able to make it to Fancy Farm, Kentucky this Saturday.”

The statement from Mr. McConnell’s office also included a photo of him smiling broadly and seated in a chair propped up by a pillow alongside his wife, the former labor and transportation secretary Elaine Chao.

In an accompanying statement, the office of the attending physician of Congress said that Mr. McConnell was continuing to recover from a fall at his home on Capitol Hill last month but that he was “not yet medically cleared” to leave the facility where he was being treated and return to the office.

The statement also said that physicians from the congressional unit visit with Mr. McConnell every day, “discussing all aspects of his rehabilitation care.” It added: “Since his discharge from hospital care, he has maintained a strenuous course of physical therapy and rehabilitation, including multiple sessions a day designed to rebuild strength and reduce the risk of future falls. His bout with childhood polio continues to be a significant factor in his mobility.”

Mr. McConnell’s extended absence has complicated matters for his party in the Senate with its small margin, particularly on the Appropriations Committee, where his vote would be important to advance bills. It has also spurred a social media storm of theories and conspiracies about his absence since he has not spoken publicly.

Multiple lawmakers and allies have said they have spoken with the senator during his convalescence and had detailed discussions with him.

Mr. McConnell’s health has been the subject of scrutiny since 2023, when he had a serious fall. He also had a few episodes where he seemed to freeze in public and be unable to speak.

In 2024, Mr. McConnell said he would not try to remain as the top Republican in the Senate. A year later, he publicly said he would not seek an eighth term this November. His current term ends on Jan. 3, 2027.