But EU citizens would face similar restrictions to British nationals if they wanted foreign relatives to join them in Britain after it left the EU unless separate rules were negotiated, she added.
Five years of residence in Britain is required for Europeans who wish to apply to stay on in the country in the future, according to the government proposal.
Yesterday's document said that...
"The truth is this country needs a new approach to Brexit".
All EU residents who qualify for settled status must apply to the Home Office - and will be breaking the law if they do not.
The Government also again rejected calls from the EU that the rights of citizens be upheld by the European Court of Justice, stating in its offer document today that the ECJ "will not have jurisdiction in the UK", but would instead be guaranteed by United Kingdom law.
The scale of the administrative task facing the Government was also laid bare on Monday, as the Home Office said it had given itself a two-year window to process applications from European Union citizens for "settled status" to protect their rights.
The EU's chief negotiator Michel Barnier called for more "clarity and guarantees" on the United Kingdom proposals while Mayor of London Sadiq Khan labeled the plan as "half-baked".
"After the United Kingdom has left the European Union, EU citizens with settled status will be able to bring family members from overseas on the same terms as British nationals", she said.
Resolving the issue is an early priority for both sides of the Brexit talks that began last week, but also threatens to cause major rows between London and Brussels.
May delivered essentially the same proposal last week in Brussels to European Union leaders, who said it did not meet all necessary criteria.
Some EU officials welcomed some elements of the proposal.
Guy Verhofstadt, the European Parliament's Brexit coordinator, said that a "number of limitations remain worrisome and will have to be carefully assessed".
The EU negotiators are adamant that its citizens should be able to continue to move freely to the United Kingdom, and have treaty rights to do so, until the United Kingdom actually leaves the union - in effect when the withdrawal agreement takes effect at the end of March 2019. Those who arrive after the cut off date could still stay in Britain (I guess that means they could apply). Brussels says they should be able to seek help from the European Court of Justice, but the government is adamant that the court will not have jurisdiction here after Brexit and says cases must be heard by British judges.
The government also unveiled plans to exclude "serious or persistent criminals, and those whom we consider a threat to the UK" - which was a potent issue for "leave" campaigners.