US senator Mitch McConnell is still not cleared to return to work, his office confirmed on Monday, six weeks after he was hospitalized after a fall at his home.

An update released alongside a new photograph of the Republican lawmaker – one of the highest-profile figures in Congress, as former Senate majority leader – said he was undergoing “intense physical therapy” and is “working hard” to get back to his duties.

“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,” McConnell, a Republican of Kentucky, said in a statement released by his office on Monday.

In the statement, he said that he wouldn’t be able to make it to Kentucky this coming weekend, for an annual Fancy Farm picnic. “There’s no place I’d rather be on the first Saturday in August than with the good people of western Kentucky, feasting on pork and mutton,” said McConnell, 84.

“I hate that I’ll miss the fun this year, but I’m sending my best wishes to the St Jerome community for a successful picnic,” he said. “As always, I appreciate all of your continued well wishes, and I’m looking forward to getting back to the Senate and to Kentucky soon.”

McConnell has been absent from the Senate and not seen in public since mid-June, when his office said he was hospitalized and recovering, but did not elaborate on his condition.

After weeks of silence, and mounting speculation about his health, McConnell’s office provided an update on 12 July, where they said that he was recovering at a rehabilitation center after having been admitted to the hospital on 14 June after suffering a fall at his home that left him “briefly unconscious”.

In the 12 July statement, the senator also disclosed that he had also been dealing with “a mild case of pneumonia” and explained the long silence about his condition by saying that “folks of my generation often hesitate to share the vulnerability that comes with growing older”.

McConnell has missed 38 Senate votes since he was hospitalized. He said last year that he would not seek re-election, and is set to retire from the Senate at the end of his term, in January.

McConnell’s office also released an image of the senator with his wife, Elaine Chao, which the caption states was from Sunday, 26 July.

Along with the statement and photograph, McConnell’s office also released a statement from the office of the attending physician (OAP) in US Congress.

“OAP physicians visit with the Senator every day, discussing all aspects of his rehabilitation care,” the OAP statement said. “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,” it added. “He is not yet medically cleared to leave the rehab facility and return to the office.”