Collecting and storing the DNA of people simply detained and not tried or convicted of a crime could draw criticism from civil rights groups.
Under President Donald Trump the US has imposed harsher immigration restrictions.
The 82-year-old Argentine pope, whose parents were of Italian immigrant stock, has made the defence of migrants and refugees a plank of his pontificate.
Setting out his priorities for the second half of his mandate, French President Emmanuel Macron said his centrist Republic on the Move party risks being seen as "bourgeois" unless it tackles the issue of immigration.
Not everyone is happy with the Nordic country's efforts to tackle growing racism against ethnic minorities.
It is the latest effort by the administration to tighten immigration, President Donald Trump's signature issue, and is aimed at restricting the movement of asylum seekers in the country and deterring more migrants from crossing the border.
Civil rights activists and lawyers say US officials subjected thousands of people to living in inadequate living conditions.
Human rights groups, like SeaWatch, have long complained about the conditions migrants have been held in detention centres run by EU-funded Libyan groups.
Lopez Obrador refused to sign the agreement, calling instead for cooperation for economic development.
Trump said ICE would focus mainly on people with convictions, including gang members, but also others.
President has announced widespread raids against unauthorised immigrants with up to 2,000 people across 10 cities identified for arrest.
Twenty-five-year-old Salvadorian Oscar Martinez Ramirez fled El Salvador with his 21-year-old wife and their daughter and decided to make the risky crossing from Mexico to the US on Sunday afternoon, according to a Mexican court report.
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