Accusations of obstruction arose last month when Trump fired FBI Director James Comey.
Sessions, a close Trump adviser during the battle for the presidency, said in his opening statement that it was a "detestable and appalling lie" to suggest he was aware of or participated in any collusion between Russian Federation and the Trump campaign. "We are not in a position to comment further".
Mr Trump's lawyer Marc Kasowitz issued a statement saying the Federal Bureau of Investigation was behind the Post story and called the leak "outrageous, inexcusable and illegal".
He denied that he recused himself from overseeing the Russian Federation investigation because he wasn't forthcoming about Russian Federation meetings.
He also said Comey should have shared his concerns about the Trump conversation with another Justice Department official, Dana Boente, who was then acting deputy attorney general, and would have been Comey's direct supervisor.
Comey had confirmed during a congressional testimony in March that the FBI was investigating possible Russian interference in the 2016 election, which included possible collusion between the country and Trump associates.
"The FBI leak of information regarding the President is outrageous, inexcusable and illegal", Corallo told CNN.
Comey testified that initial explanations that he was sacked because of poor leadership were "lies, plain and simple".
According to the Post, Mueller and his team "have also been looking for any evidence of possible financial crimes among Trump associates".
Sessions repeatedly refused to discuss private conversations with Trump on a wide variety of topics. He declined to say whether he thought Trump sought to obstruct justice, saying that would be up to Mueller to sort out. But Comey did lay out facts that a prosecutor could use to try to prove obstruction, as NPR's Domenico Montanaro noted.
He disputed that his involvement in Comey's firing violated the recusal.
"The suggestion that I participated in any collusion - that I was aware of any collusion with the Russian government to hurt this country, which I have served with honor for 35 years, or to undermine the integrity of our democratic process, is an appalling and detestable lie", he said.
Sessions hedged nearly all of his answers about whether/when he met with Russians, or why he was involved in firing Comey, or how he feels about the president's decisions, with: "I don't recall" or "I believe so" or "maybe".
The White House had no response to the news, as it has been referring all questions about the Russian Federation investigation to Trump's personal lawyer Marc Kasowitz. The New York Times reported that Trump had been waved off the idea by advisers.
Several legal experts told Reuters that Comey's testimony last week that Trump expected loyalty and told Comey he hoped he could drop an investigation of a former top aide could bolster obstruction of justice allegations against Trump.