"My first impression is the UK offer is below our expectations and this risks worsening the situation of our citizens in the UK," EU President Donald Tusk told a news conference after the second day of a Brussels summit.
European Commission chief Jean-Claude Juncker told reporters that May's offer to EU leaders over dinner late Thursday was a "first step but this step is not sufficient".
The fate of around three million European citizens living in Britain after Brexit is one of the most contentious issues in the negotiations on Britain's withdrawal from the 28-member bloc, which began on Monday.
One year after Britain voted to leave in the June 23 referendum, May promised that nobody would be forced to leave after Brexit, offering permanent rights over healthcare, education, welfare and pensions to Europeans who arrive before a cut-off date.
But she declined to say when that date would fall, offering only a window between March 29, 2017, when Britain triggered the Brexit process, and its expected departure two years later.
"It was a good start, but also not yet a breakthrough," said German Chancellor Angela Merkel, the EU's most powerful leader, adding that there was still a "long way to go".
Belgian Prime Minister Charles Michel said the proposal was "particularly vague".
German Foreign Minister Sigmar Gabriel, speaking in Paris, said the offer was "the minimum", adding "this is actually something that should be taken for granted".
"The mere fact that you won't be thrown out (of Britain) is not a convincing breakthrough, as far as I'm concerned," he said scathingly.
'Fair and serious offer'
But May defended the proposal, telling reporters at the end of the summit: "I remain of the view that this is a fair and serious offer.
"What we're saying is that those citizens from EU countries who have come to the United Kingdom, who have made their lives and their homes in the UK, will be able to stay and we will guarantee their rights in the United Kingdom."
She added: "There are some differences between that and the proposal the European Commission put out and the matter will now go into the negotiations."
Leaders said they looked forward to seeing the more technical details when Britain publishes a formal paper on the issue on Monday.
"We don't want to buy a pig in a poke," Michel said, using an old expression for wanting to inspect something closely before buying it.
May set up a clash with Brussels by refusing to allow the European Court of Justice to arbitrate any disputes over citizens' rights in Britain.
"From our point of view these will be enshrined in UK law, they will be enforced by the highly respected UK courts, and of course if this is an aspect of the withdrawal treaty it will be enshrined in international law as well," she said.
No 'families split apart'
May had previously refused to guarantee the rights of Europeans until the futures of one million British expatriates living in the rest of the EU were also secured, and she said in Brussels that her proposal depended on a reciprocal deal.
But it was also probably intended as an olive branch as she struggles to maintain her authority after losing her parliamentary majority in a snap election two weeks ago, leaving her Conservative party struggling to form a stable government and throwing her entire Brexit strategy into doubt.
May called the election to secure a mandate for pulling Britain out of the EU's single market in order to cut immigration -- a key issue in the Brexit vote -- but some of her ministers are now warning that jobs and the economy must be the priority.
Juncker was asked if he knew what form of Brexit the government in London was now seeking, to which he replied: "No."
May's proposal on citizens' rights drew a derisory response at home, with the EU migrant lobby group "the3million" declaring it "pathetic" and "backward".
London Mayor Sadiq Khan, a member of the opposition Labour party, said it "does not come close to fully guaranteeing the rights of EU nationals living in the UK".
"It is unacceptable for the prime minister to be treating EU citizens living here and contributing to our economy and society as bargaining chips," he said.
