Immigration chiefs have offered to shelve 7.5% of cases under a massive review of the backlogged US system which is aiming to deport more criminals.
Immigration and Customs Enforcement (ICE) has offered to temporarily suspend the deportation cases of around 16,500 people after reviewing more than 70% of the pending immigration cases as of mid-April, according to statistics released by the agency.
ICE officials said 2,700 cases had been shelved. The rest still require paperwork and background checks. It was not immediately clear how many immigrants had been told of the offer or how many had accepted it.
The Obama administration announced in August that about 300,000 deportation cases would be reviewed and non-criminals and those illegal immigrants who posed no public safety or national security threat would probably have their cases put on hold indefinitely.
The move was welcomed by immigrant advocates but condemned by critics who called the programme an attempt by the administration to work around Congress. Since then, however, immigrant advocates have complained that the government is offering to apply so-called prosecutorial discretion in too few instances, and that those whose deportation cases are put on the back burner still do not get a work permit.
So far, the approval rate "is a very low number", said Gregory Chen, director of advocacy for the American Immigration Lawyers Association. "You can't expect people to not be able to feed their families and have some source of income and still survive," he added.
Some say immigrants might do better by trying their luck in immigration court, where, for example, they could seek asylum.
More than half of immigrants whose asylum cases were decided by an immigration judge in the 2011 fiscal year actually won their cases, according to statistics from the Executive Office for Immigration Review, which runs the country's immigration court system.
ICE deputy press secretary Gillian Christensen said the review was ongoing. The main focus is to enable authorities to focus on deporting illegal immigrants with criminal records or those who previously ignored court orders to leave the country. "This review is designed to allow the agency to make the best use of its limited resources," she said.
Of the cases put on hold to date, the vast majority - more than 2,000 - involve immigrants who have lived in the US for a long time and have an immediate relative who is an American citizen. About 175 are children and 180 are college students or graduates who came to the US when they were under 16 and have lived in the country for more than five years, the agency said.