Murphy called the trip the "wrong decision at every level" and said it should have been canceled.
The state is trying to keep tabs on the 206 attendees and 19 workers in an effort to thwart a potential outbreak stemming from the large gathering Thursday, which included an indoor roundtable with the president that one attendee said lasted 45 minutes or more, he said.
"The actions leading up to and following this event have put lives at risk," Murphy said at an afternoon news conference. "This is very much a race against the clock."
Murphy, a Democrat, made several television appearances Monday, saying state and federal officials were still working on contact tracing. He urged anyone at the club while the president was there to quarantine for two weeks.
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"If you think you've been in touch or in the midst of someone who is COVID positive you've got to take yourself off the field," he said. "This borders on reckless in terms of exposing people."
State health officials in New Jersey have contacted more than 200 people who attended a campaign fundraiser at the Trump National Golf Course in Bedminster on Thursday, hours before the president announced he had COVID-19, as they try to contain the spread of the deadly virus.
Somerset County officials were meanwhile contacting employees who worked the event, most of whom live in the county. In a joint statement issued Sunday, the officials asked guests and employees to monitor their symptoms and, if they were close to President Trump or his staff, to quarantine for 14 days.
White House spokesman Judd Deere said the president had no contact with any donors or staff that "would be considered to be 'close' based on CDC guidelines (more than 15 minutes and within 6 feet)."
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"During the roundtable event and remarks, the President was more than 6 feet away from all participants," he said.
Dallas businessman Daniel Hux, who attended the event, said he was feeling fine Sunday, and had just undergone another test, as he and other donors had before the fundraiser.
"I'm grateful our President engaged his supporters safely while at the event," Hux said in a statement. "My prayers are with our President and the first lady."
Hux, who owns a mortgage company, declined to say where he had traveled in the interim. He said he was never within 6 feet of the president, but was quarantining just in case.
Dr. Rich Roberts, a pharmaceutical executive from New Jersey who made a video describing the event, said he sat a seat away from Trump during an indoor roundtable event, which he said involved about 19 people and lasted perhaps 45 minutes or more. Roberts did not return messages Sunday from The Associated Press about the video, which was posted on a local news site, The Lakewood (New Jersey) Scoop.
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Charlie Kolean, also from Dallas, said the coronavirus test he took upon returning home from New Jersey came back negative Sunday. He'll take another one in a few days.
Kolean, who works in investments, said from what he noticed at the event, Trump campaign members were all masked and socially distant, as were Bedminster staff, who also wore gloves.
During the photo opportunity with the president, the 25-year-old said donors were required to stand 6 feet from the president, on a marker taped to the floor.
"I know there were rumors of him being lethargic or tired. That was not the case at all at this event. He was very high energy, happy to be there. I noticed no difference in his health from previous times I've seen him," Kolean said.
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