Their climbdown came after Boris Johnson warned he will walk away from talks unless Brussels makes a “fundamental change in approach”.
EU leaders, led by the French president, infuriated Downing Street when they refused to intensify the negotiations and insisted the Prime Minister agreed to a trade-off.
But the German chancellor insisted the bloc is “ready to compromise”, including on access to Britain’s fishing waters and a demand for common standards.
Mrs Merkel claimed she would accept the UK diverging from the EU’s rulebook as long as Brussels has the ability to “react quickly” to unfair competition.
She said: “We also need to be ready to compromise. If we want an agreement, then both sides need to make a move toward each other.”
The German leader told Mr Macron his fishermen would lose all access to UK waters if he forces through a no-deal Brexit.
Mrs Merkel said: “If we can’t find an agreement with Great Britain then there will be no agreement about access to British fishing grounds, you have to keep that in mind.”
Dutch Prime Minister Mark Rutte also backed an EU retreat and praised Mr Johnson’s “positive” intervention.
He said: “We’re ready to compromise. We will not get what we want 100 per cent – that’s impossible in a negotiation, you always have to find a compromise.”
Before leaving Brussels, Mr Macron launched a stinging attack on the PM’s threat to quit the talks.
The Frenchman insisted Britain “needs a deal more than we do” and said the talks are “stumbling over everything” not just fish.
He ranted: “It’s not the job of the leaders of the 27 countries who have decided to stay in the EU to keep the British prime minister happy.” Mr Macron spooked European governments with threats to pursue a no-deal Brexit unless French boats keep the same access.
But he conceded an Australian-style arrangement would be a “win” for British fishermen.
He said: “If there is no deal, European fishermen will have no access to British waters whatsoever. That is the reality.
“If there is a deal, will the situation be the same as it is today? No, that’s for sure.”