Culture Secretary Matt Hancock has said 21st Century Fox will only be allowed to acquire the 61 per cent of Sky it doesn't already own if it sells Sky News.
He has referred Fox's bid for further consultation but said he would hope to be in a position to consult on any agreed final undertakings within the next two weeks.
The minister said he would allow Fox to participate only if Sky News was sold off to Disney or another party.
He added that the sale of Sky News would also have to mean it remained financially viable over the long-term; was able to operate as a major UK-based news provider and was able to take its editorial decisions independently.
But he warned that no deal over a divestment would mean the "only effective remedy... would be to block the merger altogether.”
He said this was "not my preferred approach" and added: "I am optimistic that we can achieve this goal, not least given the willingness 21st Century Fox has shown in developing these credible proposals.
"I want to see a broadcasting industry in Britain that is strong and effective and competitive."
Meanwhile, Hancock did give approval for Comcast's bid for Sky without the need for further consultation.
In a statement, Sky said it noted that the Secretary of State considers that the undertakings provided by 21st Century Fox have provided a good starting point to overcome the adverse public interest effects of the proposed merger that he has identified, and that DCMS (Department for Digital, Culture, Media and Sport) Officials have now been instructed to seek to agree final undertakings with 21st Century Fox.
Fox responded: "We now look forward to engaging with DCMS and we are confident that we will reach a final decision clearing our transaction."