In an open letter on Facebook, May told EU citizens in Britain that their status was her "first priority" and that the government was in "touching distance of agreement" with EU negotiators on their rights.
"I couldn't be clearer: EU citizens living lawfully in the UK today will be able to stay," she wrote.
"EU citizens who have made their lives in the UK have made a huge contribution to our country. And we want them and their families to stay."
But The 3 Million campaign group responded in a statement: "EU citizens strongly disagree that we are in touching distance of guaranteeing that their rights will be unchanged post-Brexit."
"We are barely out of the starting blocks," said Nicolas Hatton, co-founder of The 3 Million, which is fighting for the rights of EU nationals resident in Britain.
Negotiations are ongoing over what rights EU citizens remaining in Britain will have with regards to family reunions and social benefits.
EU officials have also pressed for their rights to be protected by the Court of Justice of the European Union -- a red line for May's government.
May said she was trying to ensure that EU citizens "who have paid into the UK system can benefit from what they've put in".
She said the government was developing a "streamlined" digital system to process requests for those wanting to remain, and that "we will keep the cost as low as possible".
She said a new "User Group" would bring together EU citizens and technical experts to advise on the application system.
May will address EU leaders on the state of negotiations during a working dinner in Brussels on Thursday, where she is expected to encourage them to "move the conversation" on to a future trade deal," according to her Downing Street office.
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