The Trump administration is considering suspending or limiting entry of nationals from countries with high rates of visa overstays as it seeks to clamp down on illegal immigration.

President Trump signed a memo on Monday giving the State and Homeland Security departments 120 days to come up with measures to tackle the problem.

“We have laws that need to be followed to keep Americans safe and to protect the integrity of a system where, right now, there are millions of people who are waiting in line to come to America to seek the American Dream," Trump said.

While recent attention has focused on migrants illegally crossing the border, the nonpartisan Center for Migration Studies says the visa overstays account for a higher number of illegal immigrants.

The White House said the latest figures showed 415,000 individuals were suspected to have remained in the U.S. after overstaying their nonimmigrant visas during fiscal 2018.

Officials will target nations that have overstay rates greater than 10%. Those include Afghanistan, Angola, Bhutan, Burundi, Chad, Republic of the Congo, Djibouti, Eritrea, Georgia, Laos, Liberia, Nigeria, Somalia, South Sudan, Sudan, and Yemen, according to the most recent Department of Homeland Security data.

Some have overstay rates as high as 40%, according to the White House.

The memo also tasks officials with exploring ways to stop visitors abusing the visa waiver scheme, and it lays the groundwork for using admission bonds, refundable deposits, to ensure people leave on time.

Trump has tasked two of his most senior advisers with tackling immigration concerns.

Stephen Miller, a hard-line figure from the economic nationalist wing of the Trump campaign, is focused on strengthening enforcement of existing regulations to prevent and deter migrants crossing the border.

At the same time, Jared Kushner, Trump’s son-in-law, is conducting a bigger-picture review of immigration policy that could even allow an increase in legal migration as part of a shift to a merit-based system that would end the visa lottery and family-based visas, something dismissed by Trump as “chain migration."