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Dowden said he held a "positive meeting" with football authorities -- which included the Premier League, the English Football League and the Football Association -- to "progress plans" for football to resume.
"We all agreed that we will only go ahead if it is safe to do so and the health and welfare of players, coaches and staff comes first," Dowden said in a statement.
"The government is opening the door for competitive football to return safely in June. This should include widening access for fans to view live coverage and ensure finances from the game's resumption supports the wider football family."
While the government has given the go-ahead, Dowden said it was up to football authorities to finalise the details of how they would proceed, with the government offering guidance.
"There is combined goodwill to achieve this for their fans, the football community and the nation as a whole," Dowden added.
"The government and our medical experts will continue to offer guidance and support to the game ahead of any final decision which would put these plans into action."