The episode is drawing scrutiny because of the intense interest in any dealings by Trump associates having to do with Russia or Russia-related issues, NBC News said.
The Times reported that the meeting was called to discuss a peace plan being pushed by a Ukrainian lawmaker, Andriy Artemenko, who is associated with a former Ukrainian leader backed by Russian president Vladimir Putin and advised by Paul Manafort, Trump's former campaign chairman.
Read alsoUkraine's anti-graft agency reveals details of secret ledgers with Trump's campaign chiefManafort is the subject of an FBI inquiry over his Ukraine dealings, and the FBI is also investigating whether any Trump associates colluded with the Russian campaign to interfere in the U.S. presidential election.
In an interview with NBC News Monday, Michael Cohen confirmed that Felix Sater, a former Trump associate with a criminal past, asked him to come to a meeting in New York last month, and brought along Artemenko.
"I acknowledge that the brief meeting took place, but emphatically deny discussing this topic or delivering any documents to the White House and/or General Flynn," Cohen said. "I didn't see Gen. Flynn while I was at the White House, and I didn't spend two seconds talking about this, not even one second."
The Times told NBC News that it stood by its story, saying Cohen told the newspaper he did take a sealed envelope to Flynn's office.
The Times said the peace plan was designed to lead to the lifting of international sanctions against Moscow over its seizure of Crimea, a Ukrainian territory.
Read alsoCrimea Day at Council of Europe: in 2017 Ukraine expects not just EU condemnation but acceleration of de-occupationCohen is a long-time lawyer for both Trump and his business organization. Sater worked on real estate projects with Trump's company.
"I've known Felix for years," Cohen said. "I received a phone call: 'Hey Mike, you have a few minutes? Can I meet you for coffee? You mind if I bring a friend?' Little did I know it would be a guy who wants to run for president of Ukraine."
Cohen said he had no financial interest in the meeting and was not paid to attend.
Cohen said Artemenko claims to possess evidence of corruption by the current Ukrainian leader, Petro Poroshenko. The Times quoted Artemenko as saying he had received encouragement for his plans from top aides to Mr. Putin.
Sater, who served time in prison for stabbing a man in the face with broken glass during a Manhattan bar fight, later pleaded guilty to stock manipulation and began cooperating with the FBI and the CIA, according to news reports citing court documents.
Cohen added that even if he had taken an envelope with a Ukrainian peace plan to the White House, "So what? What's wrong with that?"
The FBI and the U.S. intelligence community have been seeking to corroborate or disprove allegations in an unverified dossier compiled by a former British intelligence agent that makes a series of claims about Trump and his associates. Among them is that Cohen met with a Russian representative in Prague during the presidential campaign to discuss Russia's hacking of the Democrats.
Read alsoKremlin source tells Financial Times what made Trump shy away from RussiaIn the interview Monday with NBC News, Cohen said he was in Los Angeles when the meeting was supposed to have occurred, taking his son to a meeting with the baseball coach at the University of Southern California.
Trump's critics, he said, "are looking to malign President Trump, diminish his historic win and to undermine his presidency by claiming he didn't win — that it was given to him by the Russians," he said.