Homeland Security Secretary Jeh Johnson has said that he may limit deportations of undocumented immigrants who have not been convicted of serious crimes.

CBS reports via the Associated Press that on President Barack Obama’s orders, Johnson is reviewing U.S. deportation policy with the aim of lessening the number of deportations. The change could protect tens of thousands of immigrants who are sent back to their native countries because of immigration violations, like re-entering the country.

Two people have confirmed the possible change, including John Sandweg, former acting director of Immigration and Customs Enforcement. The other is an immigration advocate who asked to remain anonymous because of the confidential nature of the discussions. Neither would comment on specifics.

Obama has come under fire from immigration advocates for not doing enough to reform the system. The Obama administration is responsible for deporting more immigrants than any other.

Deportations of immigrants who have no criminal records, or have only been convicted of minor crimes, have specifically come under scrutiny. A recent Transactional Records Access Clearinghouse report found that only 1 percent of deportees from 2013 were drug traffickers, while most were convicted of minor crimes like traffic violations, immigration violations, or marijuana possession. Most had no criminal record at all.

The policy review wouldn’t have the impact of the legislation overhaul that immigration advocates are calling for, but it may be a start.

"The only way to truly fix it is through congressional action," Obama told reporters on Thursday. "We have already tried to take as many administrative steps as we could. We're going to review it one more time to see if there's more that we can do to make it more consistent with common sense and more consistent with, I think, the attitudes of the American people, which is we shouldn't be in the business necessarily of tearing families apart who otherwise are law-abiding."

Sources: CBS, CNN