What was planned as a two-day summit was forced into two extra days by deep ideological differences among the 27 leaders.
Overall, spirits seemed to have picked up since the talks hit rock bottom yesterday.
"It looks more hopeful than when I thought during the night: 'It's over,'" said Dutch Prime Minister Mark Rutte, a target of criticism for keeping a compromise impossible.
Rutte, defending the cause of a group of five wealthy northern nations — the Netherlands, Austria, Finland, Sweden and Denmark — sought to limit costs and impose strict reform guarantees on any rescue plan for needy nations.
He came under criticism from Macron, Italy and Hungary, whose Prime Minister Viktor Orban asked why the Dutchman had such "hate" toward him.
Rutte took it in stride.
"We are not here because we are going to be visitors at each other's birthday party later. We are here because we do business for our own country. We are all pros," he said.
Yesterday, after three days of fruitless talks and with hope dimming, Michel implored leaders to overcome their fundamental divisions and agree on the budget and recovery fund. Unanimous agreement is required.
Following discussions with leaders today, Michel adjusted his proposals and said he was "convinced, that an agreement is possible."
As he braced for a new round of talks, Italian Premier Giuseppe Conte said he was "cautiously optimistic" after a "tough" confrontations.
"We are offering a response to Europe. From this point of view, there can be no more fooling around," he said.
The coronavirus has sent the EU into a tailspin, killing around 135,000 of its citizens and plunging its economy into an estimated contraction of 8.3 per cent this year.
Spanish Prime Minister Pedro Sanchez insisted the adoption of an ambitious plan was required as the health crisis continues to threaten the continent.
"We must give an answer that gives certainty, reassurance, calm, serenity, both to companies, to workers and to all citizens in order to face this pandemic with all the guarantees," he said.
The bloc's executive has proposed a 750 billion euro coronavirus fund, partly based on common borrowing, to be sent as loans and grants to the countries hit hardest by the virus. That comes on top of the seven-year 1 trillion euro EU budget that leaders had been haggling over for months even before the pandemic.
With Macron and Merkel negotiating as the closest of partners, the traditionally powerful Franco-German alliance could not get the quarreling nations in line.
Yesterday, the leaders mulled a proposal from the five wealthy northern nations that suggested a coronavirus recovery fund with 350 billion euros of grants and the same amount in loans. The five EU nations — nicknamed "the frugals" — had long opposed any grants at all, while the EU executive had proposed 500 billion euros.
The latest compromise proposal stands at 390 billion euros in grants.
- AP
