"I want to reassure all those EU citizens who are in the UK, who've made their lives and homes in the UK, that no one will have to leave, we won't be seeing families split apart. This is a fair and serious offer," May said.
Yet many EU leaders were nonplussed by May's offer, saying there was a clear deal to leave such Brexit issues to the top negotiators, Michel Barnier for the EU and David Davis for Britain.
German Chancellor Angela Merkel said May's move was "not yet the breakthrough" that EU nations were looking for, adding "there is a long road in front of us."
Tusk agreed.
"My first impression is that the UK's offer is below our expectations, and that it risks worsening the situation of citizens," Tusk said. "It will be for our negotiating team to analyse the offer line by line."
Exactly one year after British voters chose to leave the EU and after months of political chaos at home, a weakened May sent her team into the Brexit negotiations that began Monday. The issue of citizens' rights was seen as her strongest point to make an immediate impact.
Many said she missed the mark.
"We don't want to buy a pig in a poke," said Belgian Prime Minister Charles Michel, calling May's opening "an extremely vague proposal for something that is incredibly complicated."
May promised that the fate of EU citizens would be a priority in Brexit negotiations. She laid out benchmarks for their rights and said they should be shielded from excessive harm because of the political divorce.
German Foreign Minister Sigmar Gabriel said preserving residency rights for EU citizens was such an indisputable goal that any stumbles over the issue showed how fraught the talks would be.
"The situation must be really tense if such an obvious thing is now considered as news. Of course people should at least have the right to stay, that is a minimum and personally I cannot imagine things differently," Gabriel said in Paris.
Under May's proposal, EU citizens with legal residence in the UK will not be asked to leave and will be offered a chance to regularise their situation after Brexit. May also promised to cut the burdensome bureaucracy such paperwork can involve. EU citizens now face an imposing 85-page form to tackle if they want to stay.
- AP.