Bharara also alleged that before firing him, Trump tried to cultivate relationship with him and that the pattern was similar to that of sacked Federal Bureau of Investigation Director James Comey.
Bharara was one of the 45 attorneys who were asked to resign earlier this year by the Trump administration.
"I think there's absolutely evidence to begin a case (against Trump). I think it's very important for all sorts of armchair speculators in the law to be clear that no one knows right now whether there is a provable case of obstruction," Bharara told ABC News.
"It's also true I think from based on what I see as a third party and out of government that there's no basis to say there's no obstruction," he said in his first television interview after being fired by Trump.
Bharara said, at this point, on whether or not the president has legal authority to fire or to direct an investigation, he does really get it.
"It's a little silly to me. The fact that you have authority to remove someone from office doesn't automatically immunise that act from criminal responsibility," the 48-year-old attorney argued.
"And I'll give you an example of something from a different context. If it were to be true, and this is all made up for the sake of argument...that Michael Flynn offered a million dollars to Donald Trump and said I'm going to give you this million dollars and I'm giving it to you because I want you to fire Jim Comey and then Donald Trump fired Jim Comey, which everyone agrees he has the absolute authorisation and authority to do, that would be an open and shut federal criminal case," Bharara opined.
So this argument that one keeps hearing on the TV shows that the mere fact that the president can fire an official at will does not solve the problem, the former top prosecutor said.
Coming out in defence of Comey, Bharara said nothing in the memo or in the conversations that the sacked FBI chief had with his friend at Columbia Law School was classified.
"Second, I don't understand what the privilege argument is. You know, the president's team was fully aware that the memo was going to be discussed and the conversations were going to be discussed at the hearing and had the opportunity, when many reporters asked if they would invoke executive power to try to prevent some of that from being talked about and they declined that opportunity," he noted.
"The main point that people should be focusing on, from what I can see, is that you have uncontroverted from someone who was under oath that on at least one occasion, the President of the United States cleared a room of his vice president and his attorney general, and told his director of the FBI that he should essentially drop a case against his former national security adviser. And whether or not that is impeachable or that's indictable, that's a very serious thing," he said.
It is an incredibly serious thing if people think that the President of the US can tell heads of law enforcement agencies, based on his own whim or his own personal preferences or friendships, that they should or should not pursue particular criminal cases against individuals, he said.
Talking about attempts by Trump to cultivate a relationship with him, Bharara said there were "unusual phone calls" and while reading the stories of how the president had been contacting Comey over time, he had a feeling of deja vu.
"And I'm not the FBI director, but I was the chief federal law enforcement officer in Manhattan with jurisdiction over a lot of things including, you know, business interests and other things in New York," Bharara said.
"The number of times that President Obama called me in seven-and-a-half years was zero. The number of times I would have been expected to be called by the president of the United States would be zero because there has to be some kind of arm's length relationship given the jurisdiction that various people had," he said.
Bharara said Trump called him in December when he was the president-elect.
"So he called me in December, ostensibly just to shoot the breeze and asked me how I was doing and wanted to make sure I was OK. It was similar to what Jim Comey testified to with respect to a call he got when he was getting on the helicopter. I didn't say anything at the time to him. It was a little bit uncomfortable, but he was not the president, he was only the president-elect," Bharara said.
"He called me again two days before the inauguration, again seemingly to check in and shoot the breeze and then he called me a third time when he -- after he became president and I refused to return the call," Bharara said, adding that it appeared to him that Trump was trying to cultivate some kind of relationship.
"It may be hard for viewers of yours to understand if you're a layperson and not in the Justice Department, you know, what's wrong with that. The CEO of a company wants to call a field manager somewhere in the country because he thinks he's an up-and-comer, what's wrong with that? The problem is the Justice Department is different," he said.
Bharara said it was a very "weird and peculiar" thing for the president to have a one-on-one conversation with a person has been asked to investigate various things and is in a position hypothetically to investigate business interests and associates of the president.
Bharara said hypothetically there is the authority to investigate all sorts of interests relating to a president which is why there are strict guidelines in place about what can or cannot be talked about.
"Now I'm not saying that he was going to ask me about a case, although there was some evidence in the record now that after a period of time, given the Jim Comey testimony, there's some evidence that Donald Trump didn't think anything of asking a high level law enforcement official to take a particular action that he wanted for himself on a criminal case," he said in response to a question.
2 Democrats start impeachment process against Trump
Was fired because of Russia investigation: Ex-FBI chief
'100 per cent': Trump ready to testify over Comey conversations
How much will India count with Trump?