Sen. Lindsey Graham said Sunday he will be introducing a proposal to change U.S. asylum laws, saying the only way to stop the crisis at the southern border is to toughen up asylum standards.

The South Carolina Republican said a wall and military personnel at the border helps control the flow of migrants coming from Central American countries, but won’t completely stop the problem.

“We have to change these laws so people stop coming,” Mr. Graham told Fox News during an appearance on “Sunday Morning Futures.”

“Doing what we are doing is not working … the crisis has to come to an end,” he added.

The chairman of the Judiciary Committee said lawmakers will mark up a bill once they return from recess later this month.

He wants to change the time officials can detain a minor child to more than 20 days, saying the court decision now in place requires them to be released after 20 days of detainment, long before a family’s asylum case can be decided, causing many family units (and sometimes fake families) to be released.

Mr. Graham also said the law now only lets the U.S. return minor children to Mexico or Canada instead of the Central American country from which they came, so he wants to alter the law to allow the unaccompanied minors to be returned to Central America.

The senator said the people in Central America are aware of these quirks and have been exploiting them.

Kellyanne Conway, senior adviser to the president, said Mr. Trump is ready for Congress to come up with a solution, saying so far both Democrats and Republicans have failed to act.

“We have an unserious Congress that is not coming to the table,” she said during an appearance on NBC’s “Meet the Press.”

Ms. Conway, though, did echo some of Mr. Graham’s suggestions to alter asylum laws as a way to curb the migrant flow.

The renewed push to change current U.S. immigration law comes after Senate Majority Leader Mitch McConnell, Kentucky Republican, signaled last week he’s willing to start negotiating with Democrats on a major immigration reform bill, saying something needs to get done and it will require the GOP making concessions.

Mr. McConnell said Republicans want to see action on border security and changes to the policies that create the incentives drawing migrants toward the U.S. right now — but said that will mean dealing with Democrats who control the House.

“I think it’s way past time for us to have an adult bipartisan discussion about our immigration laws and see what we can agree to,” he told reporters Thursday.

Asked whether that means he would entertain the broad “comprehensive immigration reform” approach Democrats say is necessary, Mr. McConnell signaled an openness.

“I’m willing to enter into a negotiation to see what we can do to fix the problems,” he said.