French president Emmanuel Macron urged the EU27 to agree on the recovery fund in July, as Europe faces the "moment of the truth" in the battle against the recession caused by coronavirus.
"This is the absolute priority", he added, as he gave a joint press conference with German chancellor Angela Merkel near Berlin on Monday evening.
Negotiations are set to continue at the next European Council, but Merkel has warned that no further proposals on the fund are needed.
Their get-together came ahead of Germany taking over the European Union's rotating presidency from July 1.
Both Macron and Merkel are trying to broker a deal among EU countries for a €750 billion fund to help the block recover from the coronavirus downturn.
There has been concern from the so-called "Frugal Four" countries — Austria, Denmark, the Netherlands and Sweden — about the plans, which would see the EU raise some of the money on the international markets with its triple-A rating and give it out to member states hardest hit by the crisis.
If approved, it would be the first time the bloc has pooled its debt in this way. But the richer states of the "Frugal Four" are uncomfortable with supporting the more indebted southern EU countries like Greece and Italy.