Sen. Lindsey Graham Lindsey Olin GrahamSteele Dossier sub-source was subject of FBI counterintelligence probe Hillicon Valley: Subpoenas for Facebook, Google and Twitter on the cards | Wray rebuffs mail-in voting conspiracies | Reps. raise mass surveillance concerns Key Democrat opposes GOP Section 230 subpoena for Facebook, Twitter, Google MORE (R-S.C.) said Sunday that he offered a compromise to Speaker Nancy Pelosi Nancy PelosiPelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline Trump signs largely symbolic pre-existing conditions order amid lawsuit MORE (D-Calif.) to limit the deaths of migrants making the dangerous trek to cross the U.S. border.

"I spent about an hour with Speaker Pelosi and here's the compromise: We'll start turning the aid back on to Central America. It is in our national security interest to help the Northern Triangle nations with their economy, with their rule of law problems. But if you don't turn off the magnets that attract people, which is our asylum laws, if you don't reform them, they'll keep coming," Graham said on CBS's "Face the Nation."

Graham also addressed the viral photo of a father and toddler drowned in the Rio Grande while attempting to gain access to the U.S.

ADVERTISEMENT

"Here's what I think the father believed, 'If we can just make it across the Rio Grande, and I can put one foot in America, my child and myself are gonna be in America and we're not going to get sent back,'" Graham said.

Graham added that he'd like to see asylum claims be made in Mexico at a United Nations center or in migrants' home countries so they don't have to risk their lives.

The migrants from El Salvador, Óscar Alberto Martínez Ramírez and his young daughter, Valeria, reportedly were unable to request asylum in the U.S.

"He was told by people in Central America, 'If you can put one foot on American soil, you're home free.' And this is a tragic result of that policy," Graham said.

The Hill reached out to Pelosi's office for comment on Graham's remarks.