Republicans leaders have unveiled a set of principles for immigration reform that would permit millions of undocumented immigrants to remain in the country, but deny them a special gateway to citizenship.

The speaker of the House, John Boehner, shared the principles among fellow Republican members of Congress at a retreat in Cambridge, Maryland on Thursday, as part of an effort to rehabilitate the party's reputation for obstructionism.

The principles were contained in a loosely-worded document that left the door open to giving America's 11 million undocumented workers legal status that would allow them to live and travel in the country. Crucially, the document suggests a simultaneous push to improve border security. Previously, conservatives insisted borders should be made more secure before any changes to immigration law are made.

"There will be no special path to citizenship for individuals who broke our nation’s immigration laws – that would be unfair to those immigrants who have played by the rules and harmful to promoting the rule of law," the document stated.

"Rather, these persons could live legally and without fear in the US, but only if they were willing to admit their culpability, pass rigorous background checks, pay significant fines and back taxes, develop proficiency in English and American civics, and be able to support themselves and their families (without access to public benefits)."

Undocumented immigrants who were brought to US soil as children – so-called “DREAMers” – would however be given a route to full citizenship.

The prospect of granting illegal immigrants a status that falls short of full citizenship rights will alarm some reform campaigners, who are warning it could create a sub-class. However, the principles mark a shift from the previous position taken by House Republicans, who are showing a rare appetite for compromise.

Marielena Hincapié, executive director of the National Immigration Law Center, said the changes “would go a long way toward fixing” America’s immigration system, but added that it was "unclear whether these core members of our society will eventually be able to earn citizenship".

"What happened today in Cambridge is a historic breakthrough," said Tamar Jacoby, a Republican who favours immigration reform and is president of the advocacy group ImmigrationWorks.

Jacoby said that while "vigorous debate" in the party over the proposals was now inevitable, the principles themselves constituted a significant shift in Republicans' approach to immigration.

"Strong voices from across the Republican spectrum agree with the fundamental point – the nation, and the GOP, need to act on immigration.”

• This article was amended on 31 January 2014 to correct the attribution of a quote.