Negotiations had gained momentum after foundering badly on Friday night over Dutch demands for tough supervision of how the recovery money is spent.
Mark Rutte, the Dutch prime minister, has insisted on a right to unilaterally veto grant payments to stricken countries if they do not meet reform demands.
The plan drafted overnight offers compromise wording in an attempt to address Mr Rutte's concerns, giving a nation the ability to object to payouts to a member state — but only if it does so within a three-day window. The dispute would then need to be resolved by EU finance ministers or referred up to leaders if it could not be concluded. The proposal leaves key details unresolved.
Dutch diplomats said the mechanism was a "step in the right direction" and would help Mr Rutte sell a final compromise to his national parliament.
Southern capitals will need to be convinced that the process would not significantly delay funds vital to their economic recovery.
The new "negotiating box" from Mr Michel is an attempt to prevent the leaders' first face-to-face meeting since February ending in failure, with the credibility of the bloc's collective response to Covid-19 at stake.
Friday's talks broke up after 13 hours of negotiations that laid bare division over the rules for doling out hundreds of billions of euros that the EU would borrow on the capital markets.
Mr Michel's negotiating box proposes keeping the overall size of the EU's borrowing plan at €750bn, but shifts the balance between loans and grants.
Cuts to the grants component have been made to programmes that member states had signalled that they were willing to sacrifice, including a proposed recapitalisation tool for struggling companies and an initiative to stimulate private investment.
The key area for member states such as Italy, Spain and Poland is the so-called Recovery and Resilience Facility, a new scheme that would distribute funding to individual member states. The grants available from this programme have been lifted from €310bn to €325bn in Mr Michel's new proposal.
But the frugal countries were pushing for deeper cuts to the RRF on Saturday afternoon — demanding the grants are whittled down from €325bn to around €155bn and that an additional €190bn in other spending programmes is also removed.
During a break in the summit, Austrian chancellor Sebastian Kurz told journalists there was some optimism in the talks but his government would continue to demand major cuts. The frugals' calls are being resisted by the countries worst-hit by the pandemic — like Spain, Italy, and Portugal.
Another area of dispute is over how to tie recovery money to respect for the rule of law. Hungary's illiberal premier, Viktor Orban, has threatened to veto a deal that makes respect for fundamental values a precondition of the recovery fund. He has the support of Poland's prime minister Mateusz Morawiecki.
Western European capitals are demanding tougher cash sanctions for member states such as Poland and Hungary that are accused of undermining the independent judiciary and the press.
The first day of talks on Friday dissolved in an ill-tempered dinner as leaders rounded on Mr Rutte over his intransigence on the veto.
The mood was summed up by a heated exchange over dinner when Boyko Borisov, the Bulgarian leader, accused Mr Rutte of wanting to be "the police of Europe" by handing himself the right to decide if countries' national reform plans were ambitious enough to justify EU financial support.
German chancellor Angela Merkel, who holds the EU's rotating presidency, is anxious to strike a deal on the recovery fund this month before the August break. The package is a hugely complex one to successfully negotiate.
Not only do leaders need to settle the size, governance and conditions attached to the recovery fund, but the entire process is linked to the EU's regular seven-year budget, which runs from 2021 to 2027.
Under the recovery fund component, the EU will be moving into uncharted territory by borrowing on a large scale on the capital markets.
