Amid questions over his recovery from a stroke and demands he release his medical records, John Fetterman, the Democratic nominee for US Senate in Pennsylvania, asked supporters if they had faced health challenges themselves.

He added: “I truly hope for each and every one of you you didn’t have a doctor in your life making fun of it.”

The former mayor of Braddock, now lieutenant governor, was speaking at a campaign rally in Blue Bell. He suffered a stroke in May.

His Republican opponent is Mehmet Oz, a heart surgeon who became famous on morning TV, admitted in Senate testimony to promoting diet pills that do not work, insists he does not actually live in New Jersey and is endorsed by Donald Trump.

The Oz campaign has repeatedly mocked Fetterman’s health problems. Doctored videos which seem to show Fetterman struggling to speak have spread on social media.

Fetterman still leads in polling but the gap has closed as Fetterman’s health has become a campaign issue.

Democrats insist their candidate is fine.

“I was with him Saturday in Scranton,” Bob Casey, the serving Democratic US senator in Pennsylvania, told NBC News. “He had 1,000 people! … that connection is very strong. The other side is trying to break that and they’re having real trouble because they don’t have that same connection. That’s what the race is about.”

Pat Toomey, the retiring Republican whose seat is up for grabs, told the same outlet: “If John Fetterman were elected to the Senate, and he’s not able to communicate effectively, if he’s not able to engage with the press, if he’s not able to engage with colleagues, he will not be able to do the job.”

Oz has pressured Fetterman to commit to campaign debates. Earlier this month, the Republican told reporters: “John Fetterman is either healthy and he’s dodging the debate because he does not want to answer for his radical left positions, or he’s too sick to participate in the debate.”

Fetterman then said he would debate Oz once. The event is set for 25 October.

Oz has now released his medical records. According to the Associated Press, a New York City doctor found the 62-year-old to be in “excellent health” after an annual check-up on Thursday. The AP said the Fetterman campaign did not immediately comment.

Pointing out that Pennsylvania could decide control of the Senate, now split 50-50, the Washington Post editorial board called for Fetterman to release his records.

The board wrote: “Mr Fetterman is asking voters for a six-year contract without giving them enough information to make sound judgments about whether he’s up for such a demanding job.

“We have called for full disclosure of health records from candidates for federal office in both parties, including Donald Trump and Joe Biden, and we believe Mr Fetterman should release his medical records for independent review.”

The Pittsburgh Post-Gazette has also called for Fetterman to release his records, to “reassure the public”.

The Washington Post also said Fetterman should commit to more than one debate.

It said: “Since returning to the campaign trail, Mr Fetterman has been halting in his performances. He stammers, appears confused and keeps his remarks short. He has held no news conferences.

“Mr Fetterman acknowledges his difficulties with auditory processing, which make it hard for him to respond quickly to what he’s hearing. He receives speech therapy – and we wish him a speedy, full recovery – but the lingering, unanswered questions about his health, underscored by his hesitation to debate, are unsettling.”

Speaking to NBC, the Fetterman adviser Rebecca Katz said: “John is communicating effectively with the people of Pennsylvania and running one of the best Senate campaigns in the country.

“We don’t need to speculate about whether he can be an effective leader in January, after he’s had four more months to recover. He’s effective right now.”