The Trump administration first proposed the rules in March 2018.
At the time, the American Civil Liberties Union – a civil rights group – said there is “no evidence that such social media monitoring is effective or fair”, and said it would cause people to self-censor themselves online.
US President Donald Trump made cracking down on immigration a key plank of his election campaign in 2016.
He called for “extreme vetting” of immigrants before and during his time in office.
On Friday Mr Trump vowed to impose gradually rising tariffs on Mexico unless the country curbed illegal immigration at the US southern border.