Jason Douglas in London and  Valentina Pop in Brussels

The European Union’s chief Brexit negotiator called on the U.K. to show “more ambition” in protecting the rights of EU citizens following the U.K.’s departure from the bloc after London laid out detailed proposals on the issue.

The proposals, which come just over a year after the U.K. referendum vote to leave the EU, would give EU citizens living in the U.K. as long as two years after Brexit to seek permission to stay indefinitely in the country.

London is hoping for an early success in Brexit negotiations with the EU on the rights of the more than three million EU nationals in Britain and the more than one million U.K. nationals living in the union’s 27 other member states.

Prime Minister Theresa May sketched out her plan at a meeting of EU leaders last Thursday, but it was met with a lukewarm reception.

Presenting more detailed proposals to Parliament, Mrs. May described her plan as “fair and serious” and stressed that EU citizens in the U.K. are an integral part of British society.

After Monday’s more detailed statement, Michel Barnier, the EU’s chief Brexit negotiator, called for “more ambition” from the U.K.

“EU goal on #citizensrights: same level of protection as in EU law. More ambition, clarity and guarantees needed than in today’s UK position,” Mr. Barnier tweeted.

The U.K. government said in a 24-page paper that EU nationals will able to apply for permanent “settled status” in the U.K. for themselves and their families if they have lived in the U.K. for five years or more before a specified cutoff date yet to be agreed with the EU.

The U.K. said the cutoff date will be no earlier than March 29, when it formally notified the EU of Britain’s intention to leave, and no later than withdrawal itself, expected around March 2019.

The U.K. said EU citizens will have as long as two years following Brexit to apply for residency. Settled status will confer on EU nationals the same rights as British citizens in areas including health care, education, employment and social-security benefits, the paper said.

Temporary residency will be available to EU citizens who arrived less than five years before the cutoff date and to those who arrive during the two-year grace period following Brexit, the government said.

The proposals are broadly in line with the EU’s position on citizens’ rights, but some specific areas of disagreement remain.

EU officials said they remained concerned that the U.K. said the agreement would only be enforceable in U.K. law and there would be no role for the European Court of Justice, the EU’s top court, in protecting citizens’ rights. They said the U.K. Parliament is free to make or unmake laws and therefore guarantees could be undone later.

The U.K. said however it would “be ready to make commitments in the Withdrawal Agreement which will have the status of international law.”

Guy Verhofstadt, the European Parliament’s point man on Brexit, said on Monday that while he welcomed the U.K. proposal, “a number of limitations remain worrisome and will have to be carefully assessed.”

“The European Parliament will act to protect the rights of EU citizens in the U.K. and defend the integrity of EU law, including the Charter of Fundamental Rights and its enforcement framework,” he said, in reference to the ECJ.