Cohen was responding to a question from Florida Congresswoman Debbie Wasserman Schultz, who chaired the Democratic National Committee when it was hacked by the Russians during the 2016 election.
Cohen was unable to answer the Florida Democrat's question about whether Trump knew about the DNC hacking before it happened. But he confirmed that Trump's children likely also knew about the Trump Organisation's attempt to build a Trump tower in Moscow during the 2016 election.
"The company was involved. . . which meant the family was involved," he said.
Wasserman Schultz continued: "Is it possible the whole family is conflicted or compromised with a foreign adversary in the months before the election?"
Cohen answered yes.
Wasserman Schultz, who resigned her DNC position following the hacking and release of internal emails, asked Cohen if he thought Trump was so desperate to win that he would collude and coordinate with Russia or a foreign power.
"It calls on so much speculation . . ." he trailed off. "Mr Trump, he's all about winning and will do what is necessary to win."
He continued: "I wouldn't use the word 'colluding.' Was there something odd about the back-and-forth praise with President (Vladimir) Putin? Yes. But I'm not really sure that I can answer that question in terms of collusion. I was not part of the campaign. I don't know the other conversations Trump had with other individuals."
Cohen has alleged - amid a stream of potentially damaging revelations about the President - that Trump knew in advance that the anti-secrecy organisation WikiLeaks planned to publish hacked Democratic National Committee emails, and he will describe the president as a "racist," a "conman" and a "cheat," according to a copy of his written testimony.
The WikiLeaks allegation is perhaps the most explosive in the written testimony, speaking to the core of Special Counsel Robert Mueller's probe into whether the Trump campaign coordinated with Russia to influence the election. Mueller already has alleged that Russian military officials hacked the emails before they were published online by groups including WikiLeaks.
Earlier, Cohen provided to Congress three documents called "statements of financial condition," which he said Trump had prepared to show potential lenders that he was worthy of a loan. Cohen said that these three statements - from 2011, 2012 and 2013 - were shown to Deutsche Bank, as Trump sought a loan to purchase the Buffalo Bills football team. Trump, in the end, did not buy the team.
These statements were not rigorously audited financial documents. Instead, they amounted to Trump's own estimates about what he was worth and what he owed. Trump himself was the main source of the data.
But the 2013 statement showed something remarkable.
That year, Trump rapidly increased his own estimate of his net worth - from US$4.6 billion to US$8.6 billion.
The reason was not a new building or a big business success by Trump. Instead, Trump simply assigned a massive dollar value - US$4 billion - to his own brand, and then counted that brand among his assets, as if it was a building or a golf course. The result was that his net worth nearly doubled.
In his statement, Cohen said that these statements were part of a pattern of Trump exaggerating his net worth, when it benefitted him.
"It was my experience that Mr Trump inflated his total assets when it served his purposes," Cohen said.
Congressman Jim Jordan, an Ohio Republican and the panel's ranking Republican, made clear in his first exchange with Cohen what Republicans line of attack will be at the hearing: Cohen is a disgruntled employee, upset that he couldn't get a job in the Trump White House.
Jordan opened his questioning of Cohen by walking the President's former personal lawyer through a litany of wrongdoing - including tax and bank fraud - to which he has pleaded guilty, but has nothing to do with Trump. He highlighted a Twitter account that he said Cohen had created, "Women For Cohen," that seemed to promote Cohen's personal brand.
"Was that done to protect the President?" Jordan sneered.
Cohen asserted a woman at an outside firm, RedFinch, had created the account to help blow off steam during the heart of the high-stakes presidential campaign.
"We were having fun," Cohen said.
Jordan then turned to his main line of attack.
"You worked for [Trump] for 10 years, Mr Cohen. How long did you work in the White House?" Jordan asked.
"I never worked in the White House," Cohen responded.
"That's the point, Mr Cohen, isn't it?" Jordan asked. "You wanted to work in the White House. You didn't get brought to the dance."
Cohen insisted he was offered White House jobs and said he could tell a story of Trump "reaming out" chief of staff Reince Priebus because Trump wanted him to work in the White House counsel's office.
"Mr Jordan, all I wanted was what I got, to be personal attorney to the president," Cohen said.
Also in earlier testimony, Cohen said "there is no doubt" in his mind that Trump was acutely aware that Stormy Daniels, an adult-film actress, was being paid to keep silent about an alleged affair she had with the President, payments orchestrated through Cohen.
He brought a series of check images with him to show how and when Trump incrementally reimbursed him for the US$130,000 payment to Daniels - showing that Trump was intimately involved with the scheme, even while president.
One cheque for US$35,000, dated March 17, 2017, was issued from a trust account belonging to Trump, and signed by his son, Donald Trump jnr. Another dated August 1, 2017, was from Trump's personal account - and signed by the President himself.
Cohen said the payments were made directly because they were "declaratively a retainer for services that would be provided for the year of 2017."
But "there is no retainer agreement," he noted.
Trump jnr offered his first response to Cohen's testimony on Twitter. He has not addressed any of Cohen's direct accusations, including Cohen's claim that he signed one of the cheques to Cohen reimbursing him for his payments to Daniels. Instead, Trump jnr brought the snark, tweeting, "This sounds like a breakup letter . . .and I'm keeping your sweatshirt."
Earlier from Hanoi, President Trump had weighed in via Twitter:
"Michael Cohen was one of many lawyers who represented me (unfortunately)," Trump wrote on Twitter. "He had other clients also. He was just disbarred by the State Supreme Court for lying & fraud. He did bad things unrelated to Trump. He is lying to reduce his prison time. Using Crooked's lawyer!"