The government says it is "opening the door" for the return of professional football in England in June.
Culture Secretary Oliver Dowden said Thursday's meeting with the Football Association, Premier League and English Football League had "progressed plans".
He added that plans for the sport to resume should "include widening access for fans to view live coverage".
Meanwhile, England's deputy chief medical officer said any return would be "slow" and "measured".
The Premier League met on Monday to discuss "Project Restart" and hopes for a return to action on 12 June, with matches played behind closed doors.
"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," said Dowden.
"It is now up to the football authorities to agree and finalise the detail of their plans, and there is combined goodwill to achieve this for their fans, the football community and the nation as a whole.
"The government and our medical experts will continue to offer guidance and support."
He added that plans to return should "ensure finances from the game's resumption supports the wider football family".
The next meeting of Premier League clubs will take place on Monday, when top-flight players may return to initial group training under social distancing protocols.
Footballers have so far been limited to individual training but Premier League bosses hope a first phase of team training, under strict guidelines and restricted to 75 minutes, can begin next week.
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England's deputy chief medical officer, Jonathan Van-Tam, said: "There will be small, carefully measured, step-wise approaches to see what can be achieved safely. The first of those is to return safely to training, still observing social distancing.
"We will have to see how that goes before we can even think about moving on to the return of competitive football matches."
Monday's meeting will come after a weekend when the Bundesliga, Germany's top flight, becomes the first major league to restart.
The Premier League has been suspended since 13 March because of the Covid-19 pandemic and most teams have nine fixtures left to play.
Brighton had a third player test positive for coronavirus earlier in May and boss Graham Potter is wary about a return to action.
"We are in uncharted territory. It's a hugely complex situation," he said.
"It's very difficult to call one day to the next. The general will from all the clubs is to play out the season as close to the format as possible. Whatever date that is remains to be seen.
"We are sanitising the environment. The players are not coming in for any length of time.
"It will be as safe as it is made to be. The challenge will be when [we have] contact, larger groups and different teams. We need to see where we are on Monday and then Tuesday."
He added: "There are concerns, of course. We have come out of lockdown. The situation is not totally resolved.
"I have a young family. My wife's family has health issues. We are human beings."
Meanwhile, the Premier League confirmed clubs had decided that short-term contract extensions could be agreed with players whose deals run out on 30 June, with the season set to go beyond that date.
Clubs and players will now have until 23 June to agree extensions which run until whenever the campaign is scheduled to finish.
Premier League chief executive Richard Masters said it was decided "to ensure as far as possible that clubs complete the season with the same squad they had available prior to the suspension of the campaign".
Elsewhere, six League One clubs have united to express their determination to finish the season.
Peterborough chairman Darragh MacAnthony has released a statement on behalf of Posh, Oxford, Sunderland, Fleetwood, Portsmouth and Ipswich.
League One clubs are due to meet with the EFL board on Friday to discuss options for completing the season.
Dan Roan, BBC sports editor
The fact the government summoned the three football bodies to a meeting together tells its own story. Ministers want football to think collectively during this crisis, and act in the interests of the whole game. And to understand that any government financial bailouts for the sport are highly unlikely.
The Premier League was reminded that if its season does resume next month, it will be expected to do what it can for clubs in the EFL and for grassroots football. And to ensure that, while honouring contracts with its broadcast partners, as many matches as possible are shown free to air, so that as many people as possible can watch them.
With the Premier League lobbying government to scrap the idea of neutral stadiums to keep their clubs happy, ministers are now asking for something in return.
It was significant today that despite continued police concerns over the risk of fans gathering outside grounds once matches resume, the government reinforced its support for the resumption of matches.
But it also warned that games will only take place if the phased return to training goes to plan, and the sense is that 'Project Restart' still hangs in the balance.