Mr Comey also testified in his written testimony that Mr Trump, in a unusual private encounter near the grandfather clock in the Oval Office, pushed him to end his investigation into former national security adviser Michael Flynn.
"It's my judgment that I was sacked because of the Russian Federation investigation", he told senators.
Describing that dinner, he said, "My common sense told me that what was going on is, either he thought or someone told him, "you have already asked Comey to stay, and you did not get anything for it.' And the Trump had demanded my 'loyalty".
"Today, Mr. Comey admitted that he unilaterally and surreptitiously made unauthorized disclosures to the press of privileged communications with the president", Kasowitz said, speaking to reporters at the National Press Club in Washington.
The National Rifle Association's news outlet NRATV spun former FBI Director James Comey's testimony to the Senate intelligence committee to President Donald Trump's advantage by flatly lying about what Comey said.
Trump ousted Comey last month, saying he was thinking of "this Russian Federation thing" when he chose to dismiss the chief of the country's top criminal investigative agency while he was leading its Russian Federation probe.
US President Donald Trump is yet to publicly respond to James Comey's testimony, leaving it up to his lawyer and sons.
Some opposition Democrats say Trump's requests to Comey to drop the Flynn probe amounts to obstruction of justice, an impeachable offense similar to that leading to the 1974 resignation of former President Richard Nixon.
"We will leave it to the appropriate authorities to determine whether these leaks should be investigated along with all the others that are being investigated", Kasowitz said. She did take issue, though, with Comey's claim that Trump is less than honest.
London Mayor Khan suggests calling off Trump state visit to Britain
And as the president of the world's superpower, Mr Trump should be advised to do the same: to think before he tweets. Khan said the United States and Britain were "close allies" and they should continue to work closely together.
"In his opening written statement, Comey recounted how at a White House dinner in January shortly after Trump assumed power, the president told him, "'I need loyalty, I expect loyalty.' I didn't move, speak or change my facial expression in any way during the awkward silence that followed.
"Although Mr. Comey testified he only leaked the memos in response to a tweet, the public record reveals that the New York Times was quoting from these memos the day before the referenced tweet".
The president himself was uncharacteristically restrained during the Comey hearing. Comey also called Trump and the White House "liars" and said they had defamed the Federal Bureau of Investigation.
"If there were some "satellite" associates of his who did something wrong", Mr Comey said the president told him, "it would be good to find that out".
"So in essence the president agreed with your statement that it would be great to have an investigation if all the facts came out and you found nothing".
"The president feels completely vindicated", Kasowitz added when he stepped before the cameras.
Given that the former director's testimony is going cast a shadow over the Trump presidency for months, if not years, the White House counterattack is nearly certainly only just beginning.
"He is eager to continue to move forward with his agenda", said Marc Kasowitz, hired by Trump as his personal lawyer to deal with issues linked to the Russian Federation investigation, after Comey's statement was released.
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