US Senator Mitch McConnell says absence due to fall and pneumonia

US Senator Mitch McConnell says he will not be returning to the Senate "quite yet" after suffering from a fall and "a mild case of pneumonia".

It is the first statement from the 84-year-old Kentucky Republican after weeks of speculation about his health, following his admission to hospital in mid-June.

In addition to the statement, McConnell released a photo of himself with his wife holding what appeared to be Sunday's Washington Post newspaper.

"You all know how folks of my generation often hesitate to share the vulnerability that comes with growing older," he said in a written statement from his office on Sunday.

"Even in the public eye, I feel that same instinct – I can't help it."

McConnell also referenced his childhood polio and the ongoing "mobility challenges" he faces as a result.

"They haven't exactly gotten easier to manage with age. And last month, I took a fall which landed me in the hospital," he said.

"My doctors have confirmed that I didn't break any bones or suffer a concussion. I didn't have a heart attack or a stroke. I don't have any tumours or haemorrhages. But I was briefly unconscious and was taken to the hospital," the statement read.

"While receiving excellent care over the past several weeks, I've also had to deal with a mild case of pneumonia."

The statement said McConnell had been moved from hospital care to a rehabilitation centre.

"As much as it frustrates me, this process takes time. And on the advice of my doctors, I won't be able to return to the Senate floor to vote quite yet."

Calls for information about the condition of McConnell, who holds the title of the longest-serving Senate party leader in US history, grew as his hospital stay approached the one-month mark this week.

He was admitted for treatment on 14 June, according to his staff.

His aides did not give any details about the reason for his hospital stay, or what kind of treatment he was receiving.

The Kentucky senator's team said on 2 July he was "receiving excellent care" and "continues to improve". But aside from that statement and some reported phone calls with a handful of people, he did not appear in public or in photos.