"We need to reach an agreement over the summer, I absolutely cannot imagine any other option," said Merkel, whose country has just taken over the rotating EU presidency for six months.
The proposed fund would controversially be financed through shared EU borrowing, which marks a stunning U-turn for Germany after years of opposition to debt pooling.
Together with Macron, Merkel sketched out the backbone of the 750 million-euro ($840-million) fund proposed by von der Leyen to bolster the bloc's economy.
It was the clearest attempt yet by the bloc's most powerful leaders to spur the EU executive to find ways to fix the disunity displayed in the crisis, especially in its earliest days.
The cabinet is expected to pave the way for the agreed temporary cut in value-added tax, cash handouts for parents and bigger incentives to buy electric cars, the sources said.