President Trump on Friday again claimed that his response to the coronavirus was hindered by the Obama administration, which left office three years ago.

Mr. Trump attacked Mr. Obama, who served with Mr. Trump’s likely Democratic challenger, Vice President Joseph R. Biden Jr., in two posts on Twitter.

“For decades the @CDCgov looked at, and studied, its testing system, but did nothing about it,” Mr. Trump wrote. “It would always be inadequate and slow for a large scale pandemic, but a pandemic would never happen, they hoped. President Obama made changes that only complicated things further.

“Their response to H1N1 Swine Flu was a full scale disaster, with thousands dying, and nothing meaningful done to fix the testing problem, until now,” he continued. “The changes have been made and testing will soon happen on a very large scale basis. All Red Tape has been cut, ready to go!” he wrote.

Sign Up For the Morning Briefing Newsletter

Mr. Trump was not specific about what changes President Barack Obama made to “complicate things further,” but at least one regulatory change previously discussed by Mr. Trump and his C.D.C. director was never put into effect. Mr. Trump had leveled that criticism last week.

A spokesman for Mr. Obama declined to comment.

In his tweet, Mr. Trump may have been referring to actions taken by the Food and Drug Administration during the Obama administration, when the agency proposed regulating high-risk lab-developed test with a premarket review. But that idea applied outside of emergency situations and was never finalized.

The F.D.A. took the position that during a public health emergency, nongovernment labs should come to it before doing tests. But at any time, the agency was prepared to suspend that practice, as it did in recently when it gave laboratories and hospitals around the country the go-ahead to conduct tests that had been limited to those analyzed by the C.D.C.

Slideshow by photo services

Meanwhile, an Australian official who posed with Ivanka Trump and Attorney General William P. Barr on March 6 has tested positive for the coronavirus, officials said. Peter Dutton, the home affairs minister, said in a statement that he woke up with a fever and a sore throat, and later a test confirmed the diagnosis.

Mr. Trump and Vice President Mike Pence met over the weekend with a Brazilian official at the president’s private club, Mar-a-Lago, who later tested positive for the virus. After the revelation on Thursday, White House officials said the president would not be tested.

The White House has said that Mr. Trump barely interacted with the Brazilian man, despite a photo of them standing next to one another, and that the president has not been tested. Still, the guidelines from health officials suggest that Mr. Trump should be in a self-quarantine because of the exposure.

On Thursday, Dr. Anthony S. Fauci, a member of the administration’s coronavirus task force, refused to say whether the president should be tested when he spoke to reporters outside the White House.

“I am not going to comment on an individual who has a very competent physician,” Dr. Fauci said.