It comes after a series of claims regarding Trump's former National Security Adviser Michael Flynn and his campaign team and their links to Russia.
The President and his team have strongly denied all the reports, calling them "nonsense."
In an interview with NBC's Matt Lauer, Conway claimed the revelation that Gen Flynn had lied to Vice President Mike Pence - who then went on television and insisted he had not discussed sanctions with the Russian ambassador - was the key factor in his resignation.
"I think misleading the vice president really was the key here," Conway said.
"But wait a second," Lauer replied. "You're saying that was the straw that broke the camel's back, but the White House knew about that last month when the Justice Department warned the White House that Gen Flynn had not been completely honest in characterising that conversation with the Russian ambassador. And they even went further to say that as a result of that dishonesty, he was at risk for blackmailing by the Russians."
"Well, that's one characterisation, but the fact is that Gen Flynn continued in that position, and was in the presidential daily briefings, was part of the leader calls as recently as yesterday," Conway said. "As time wore on, obviously the situation had become unsustainable ..."
"Kellyanne that makes no sense," Lauer interjected. "Last month, the Justice Department warned the White House that Gen Flynn had misled them, and as a result he was vulnerable to blackmail. And at that moment, he still had the complete trust of the president?"
"Matt, I'm telling you what the president has said, which is that he's accepted Gen Flynn's resignation and he wishes him well, and that we're moving on," Ms Conway answered.
Later, Press Secretary Sean Spicer told reporters Trump's trust in Gen Flynn had "eroded" over the weeks between the Justice Department's warning and his decision to step down.
