European Commission chief Jean-Claude Juncker said 14 or 15 countries had agreed to step up their national contributions - which still leaves almost half of the bloc undecided or opposed.
And he later claimed the current United Kingdom position on its post-Brexit relationship with the bloc was "based on an illusion", hitting out at the United Kingdom trying to get a bespoke deal.
"It seems like the "cake" philosophy is still alive".
May and 11 of her cabinet members spent eight hours in a marathon meeting at Chequers, the official country house of the British prime ministers.
"I don't want a new divide in Europe, we have enough of that".
"We, in any case, do not want our contribution to rise", he said.
"The party and the country are looking for clear direction, and formulation of the British position must take as long as it requires", he said, adding it would have to be clear in time for an European Union summit beginning on March 22.
May is meeting with her most senior ministers to try to force them to agree the outline of a trading policy that would see the United Kingdom remain close to European Union rules in many areas - such as carmaking and data sharing - while breaking away partially or fully in others, an approach known as the "three baskets".
Asked about the Chequers meeting, Jean-Claude Juncker, the European Commission president, said: "I haven't seen the results so I can't comment on it".More news: Russia Using Syria's Civil War to Showcase Its Stealth Jet Sukhoi 57
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Dutch Prime Minister Mark Rutte disagreed, a sign of divisions between leaders that could presage bitter wrangling during months of budget discussions.
He said: "Yes we are aligned as 27 and yes we have very close ties with Britain".
" I want Britain to be able to negotiate its own trade agreements", she said.
"Technically, because we're leaving the European Union, we can't be in the customs union we are in now", Emily Thornberry said.
Meanwhile, Mr Varadkar added: "It's not a la carte".
Spanish Prime Minister Mariano Rajoy added: "I think Spain must be open to put more resources".
"Those who want to restrict the European Union budget to 1 percent of Gross National Income of the 27 countries instead of the current 1.13 percent should know that such a cut would mean cutting cohesion and agriculture funds by 15 percent or else to reduce other policies by 45 percent", he said.
Among the others in attendance were the leaders of The Netherlands, Spain, Portugal, Italy, Bulgaria.
British Prime Minister Theresa May is excluded from the meeting in Brussels, the latest in a series of special European Union summits aimed at charting a roadmap following Britain's shock 2016 vote to quit the bloc.
The intervention comes at a critical time in the Brexit process, with May's authority under pressure and time for negotiations running short.