Boss Carlos Watson told broadcaster NBC that the firm was “open for business” again and this was its “Lazarus moment” – referring to the biblical character brought back to life by Jesus.
Ozy shut on Friday after reports its co-founder had deceived potential investors during a conference call.
Major advertisers cut ties and its chairman Marc Lasry stepped down.
On Monday, Mr Watson told NBC that the previous week had been “traumatic” and “heartbreaking”.
However, he said the media firm had a change of heart: “Over the weekend we spoke to advertising partners, we talked to our readers, our viewers our investors.
“I think Ozy is part of this moment. I think what we do… has a place.”
Launched in California in 2013, Ozy Media produces left-leaning podcasts, television series and events. The firm has won an Emmy for its work.
In late September, the New York Times reported that co-founder Samir Rao impersonated a senior leader at YouTube during a conference call with Goldman Sachs in February. At that point the investment bank was considering making a $40m investment in the media company.
Mr Rao reportedly claimed that Ozy’s videos were highly popular on YouTube.
According to the Times, the investors realised something was wrong and did not go through with the deal. Mr Watson later apologised and Mr Rao was allowed to stay at the firm.
Amid growing scrutiny last week, Ozy began an internal investigation and Mr Rao took a leave of absence.
It prompted veteran journalist Katty Kay – who joined Ozy in June after 30 years at the BBC – to quit, followed by Mr Lasry. Ford and Ally Financial cut ties with the media firm, amongst other advertisers.
Mr Watson told NBC that what Mr Rao had done was “sad” and “wrong”.
He accepted that it was a “fair question” as to whether people would be able to trust him again as chief executive. The latest scandal is just one in a long string of allegations that has emerged, including claims the firm inflated its audience figures.
Mr Watson said he had been given “incredibly bad advice” last week “to go silent”, when he should have engaged with the press.
As a result, he said “half truths”, inaccuracies and “cheap shots” were reported in the media and that Ozy was not a “house of cards”.
Mr Watson added Ozy intended to “own” the mistakes that had come to light around its use of data and marketing.
The firm could struggle to get back on its feet. It has lost most of its staff and only two people are currently on its board – Mr Watson and Michael Moe, founder of the Silicon Valley investment company GSV Holdings, which backs Ozy.
In a statement, Ozy told the BBC it was reaching out to its team to encourage them to return. It added that its newsletters will resume this week and TV production at the end of the month.
The firm added that several advertising partners had expressed excitement about the firm re-launching and intended to meet with Ozy in the coming days to discuss “next steps”.
Ozy spokesman Phil Singer told the BBC: “The bottom line is that we hit a bump in the road, but are committed to getting past this moment and renewing our commitment to being the kind of media company that delivers amazing content about topics and people that are too often overlooked.”