Two Republican senators used a Thursday meeting at the White House to lobby President Trump to ensure a bill doing away with the diversity visa lottery is pushed through Congress, according to a source with knowledge of the discussion.

A senior Senate aide told the Washington Examiner that Sen. Tom Cotton of Arkansas and Sen. David Perdue of Georgia are working with Trump "to make sure" their RAISE Act is "included in any immigration solution" to the Deferred Action for Childhood Arrivals program.

Cotton and Perdue introduced the RAISE Act this year to create a merit-based immigration system. It would eliminate the diversity visa lottery, which authorities say was used by the suspect behind this week's terrorist attack in New York to enter the U.S. in 2010.

Conservatives are pushing for tougher immigration measures in a bill that would create a legislative version of DACA, which Trump has said he would rescind by next year. DACA allows younger immigrants who were brought to the U.S. illegally as children to stay and work in the U.S., but most Republicans want that program, created by former President Barack Obama, to be authorized in the legislation.

Cotton and Perdue were part of a delegation led by Senate Judiciary Chairman Chuck Grassley that met with Trump on Thursday.

House Minority Leader Nancy Pelosi has ardently opposed the idea of border funding or implementing a merit-based point system for employment-based green cards.

Grassley has indicated his committee hopes to see some merit-based reforms in a DACA bill, though he has not picked up the RAISE Act, which was reintroduced with revisions three months ago and endorsed by Trump.

Perdue's spokesperson told the Washington Examiner they ought to be able to coalesce support for the bill from Republicans who remain on the fence, as well as Democrats.

"All Republicans as well as many Democrats, should be supportive of this solution," the spokesperson said.

Trump attacked Democrats and Senate Minority Leader Schumer over the New Yorker's support for the diversity visa lottery, which allowed the suspect in Tuesday's terror attack to get into the country. Schumer helped propose the diversity visa lottery in 1989 as a House member, and a different version of the proposal was later included in Sen. Ted Kennedy's immigration reform bill in 1990.