Texas governor Rick Perry has suggested that the comedian Joan Rivers might not have died during a routine medical procedure had the New York outpatient clinic treating her been subject to the same kind of stringent standards required by Texas’s controversial new abortion laws.

Rivers died, at the age of 81, in hospital earlier this month, a week after suffering a cardiac arrest during what was expected to be a minor throat procedure.

Last year, amid intense protests, Perry signed into a law a bill containing some of the nation’s most stringent abortion restrictions. The bill includes the requirement that abortions be performed in ambulatory surgical centres and has led to the closure of about half of Texas’s clinics, many of which were unable to upgrade their facilities.

Perry and other Republican supporters of the bill have maintained that it is designed to safeguard women’s health. Critics have argued that it is simply a way for conservative lawmakers to restrict abortions. Parts of the law have been the subject of litigation that could ultimately end up before the supreme court.

“It was interesting that when Joan Rivers, and the procedure that she had done, where she died – that was a clinic. And I’m just – it’s a curious thought that if they had had that type of regulations in place, whether or not that individual would be still alive,” Perry said on Sunday in response to a question from an audience member during a keynote session at the Texas Tribune Festival in Austin.

Despite Perry’s comment appearing to advocate for such centres, Rivers was treated at a facility which has been described as an ambulatory surgical centre. The circumstances of her death are still mired inuncertainty, claims and counter-claims.

Pro-choice campaigners reacted angrily to Perry’s words. In an email to the Associated Press Heather Busby, executive director of NARAL Pro-Choice Texas, wrote: “The reality is that complications happen in all areas of medicine. There’s risk inherent in just about anything.

“You could have a heart attack and die while having your wisdom teeth removed. Should we outlaw wisdom teeth removal?”

Sounding subdued earlier in the session, Perry declined to comment on his indictment by a grand jury last month on abuse of power charges related to his threat to veto funding for a public integrity unit, or his decision that Texas taxpayers would part-fund his legal defence.

“It’s in the hands of the lawyers now … there’s nothing new to add to it,” he said.

Asked by Texas Tribune chief executive and editor-in-chief Evan Smith to name up to three mistakes he has made during his state-record 14 years as governor, Perry poked fun at the “oops” moment that derailed his 2012 presidential bid, when he was unable to name all three federal agencies he wished to eliminate.

“Three’s a bit of a stretch for me,” he said.

In the end, he named one – mandating the HPV vaccine for young girls.

Perry said he was laying the groundwork for a potential second run at the White House in 2016. He has tried to remake his image, using the recent border crisis to boost his national profile, making numerous trips across the country and abroad and reportedly sought the help of advisors including the policy director of Mitt Romney’s 2012 campaign”. He said that he decided two years ago that if he were to run again he would be fully ready.

“I went through a very humbling and a very frustrating process, in 2011-2012, I learned some, for me, very harsh lessons, the least of which that you must be very physically fit, mentally fit if you’re going to run … I was not prepared and it was obvious,” he said.

Asked when he will reveal his intentions, he said: “I don’t know, I’ll make that decision in 2015”.

Perry, who is stepping down as governor at the start of next year, predicted that the performance of Republicans in November’s midterm elections would be highly influential as to who runs for the party’s nomination for the White House.

Speaking with the Washington Post reporter Dan Balz during a keynote session a day earlier, Ted Cruz, a US senator from Texas, hinted that he would determine whether to stand for the Republican presidential nomination in the first half of next year.

One year on from the government shutdown that furloughed 850,000 workers and cost billions of dollars, Cruz is in no doubt about its negative impact: it led to him being unfairly demonised by the liberal media.

“I get that people like to paint a caricature that Cruz doesn’t compromise,” the Texas senator said. “I’m absolutely happy to compromise with anyone … if they are shrinking the size of the federal government.”

Cruz said that the mainstream media has habitually depicted prominent Republicans as “stupid” or “evil” and said he had been portrayed as “a wild-eyed lunatic with dynamite strapped to his chest”. The Tea Party darling was highly influential in the shutdown that was prompted by conservative Republicans attempting to defund Obamacare. But he insisted on Saturday that the flashpoint was the fault of Democrats in Washington, especially President Obama, who, he said, were the ones refusing to compromise.

He criticised the president’s “fundamentally unserious” approach towards tackling Islamic State (Isis) militants in Syria and Iraq and called for strong military action.

“I don’t think it is our job to engage in nation-building … we shouldn’t be trying to turn Iraq into Switzerland,” he said.

Cruz also slammed Obama for saying he will delay potential executive action on immigration reform until after November’s mid-term elections.

“I think it’s one of the most cynical acts I’ve ever seen,” he said. “He knows the American people strongly disagree and he’s basically trying to trick them after the election.”

Speaking after Cruz, Wendy Davis, a Democratic state senator from Fort Worth who rose to fame for filibustering against the abortion bill, said she was confident of victory over her Republican opponent, Greg Abbott, in November’s gubernatorial election.

Davis went on the attack against Abbott in a televised debate on Fridaybut polls suggest the Texas attorney general has a commanding lead.

“I trust our numbers, I trust our message and most importantly I trust the people of our state,” she said.