European Union nationals living in Britain said Theresa May "can do better" than her letter promising the Government will make it as easy as possible for them to stay after Brexit.
Campaign group the3million, which represents EU nationals in the UK, called on the Prime Minister for an "open dialogue about the real issues".
One of the recipients of the note published on Facebook and posted to 100,000 of the three million EU nationals living in the UK, Hedwig Hegtermans, suggested it was designed to break the deadlock in Brexit negotiations.
EU leaders are set to reject British demands to move forward to the second stage of negotiations, on trade, at a European Council summit which begins on Thursday, because "sufficient progress" has not been made on withdrawal issues, including citizens' rights.
Ms Hegtermans said: "This letter might be addressed to us but the intended audience is the EU heads of state - to help move to phase two of the negotiations."
The3million also "strongly disagree" with Mrs May's claim that Britain and the EU are within "touching distance" of agreement on citizens' rights.
The group's co-founder Nicolas Hatton said: "We are barely out of the starting blocks.
"For the past year, we have unsuccessfully tried to meet with David Davis and Theresa May.
"We have also made detailed objections to the proposed 'settled status' which have been read but seem to have been comprehensively ignored."
One of the group's objections to the "settled status" Britain is offering EU nationals who are already in the UK is that it could water down their rights to family reunification, which is also believed to be a sticking point in negotiations.
But Mr Hatton noted a passage in the PM's letter stating "we want families to stay together".
Calling for dialogue, he said: "Perhaps this letter will open the door."