"I can assure you that any goodwill that might have existed in the committee with Michael Cohen is now gone," the North Carolina Republican told reporters Tuesday on Capitol Hill.
Burr reiterated that his committee had "no factual evidence of collusion between the Trump campaign and Russia," but that he wanted to interview Cohen before the former lawyer for President Donald Trump reports to federal prison next month.
"I would prefer to get him before he goes to prison, but you know, the way he's positioning himself, not coming (to) the committee, we may help him go to prison," Burr said.
Cohen's attorney Lanny Davis said Monday the latest postponement was "due to post surgery medical needs."
Burr took issue with Cohen's excuse on Tuesday, appearing to reference a widely circulated tweet saying Cohen was at a lengthy dinner over the weekend.
"He's already stiffed us on being in Washington today because of an illness," Burr said. "Yet on Twitter, a reporter reported he was having a wild night Saturday night eating out in New York with five buddies, didn't seem to have any physical limitations. And he was out with his wife last night."
Davis disputed Burr's comments as "inaccurate" in a statement Tuesday evening, saying Cohen had committed to testifying on a voluntary basis later this month.
"Mr. Cohen was expected to and continues to suffer from severe post shoulder surgery pain, as confirmed by a letter from his surgeon, which was sent to Senator Burr and Senator (Mark) Warner," Davis said. "The medication Mr. Cohen is currently taking made it impossible for him to testify this week."
"We watched them the whole time," she said. "When the dinner was over ... as Cohen was walking out, he greeted several tables."
In his statement Tuesday evening, Davis said it was possible for Cohen "to be in pain and still have dinner in a restaurant with his wife and friends."
Burr, in his comments to reporters earlier in the day, said he declined generally to specify who his committee had or had not subpoenaed, but said Cohen "clearly rises to one of the people that I would go to every length I could to make sure that we got his testimony."
Later Tuesday, Burr said he had been talking with Cohen's attorney "all day," and when asked if he thought Cohen would come before investigators now, Burr said, "I thought he was going to come in today."
CNN's Evan PereKristin Wilson, Marshall Cohen and Laurie Ure contributed to this report.