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The Trump administration asked the Supreme Court to allow a rule limiting asylum claims to go into effect nationwide while a lower court ruling blocking it is appealed.

A federal judge had blocked the Trump administration rule, which dramatically limits the ability of Central American migrants to claim asylum if they enter the US by land through Mexico, nationwide. Earlier this month, the 9th US Circuit Court of Appeals dialed back the nationwide injunction, saying that it can only apply to migrants claiming asylum in California and Arizona, states that fall under the Ninth Circuit’s jurisdiction.

In its filing Monday, the administration laid out its case for the rule, arguing that, among other things, it “alleviates a crushing burden on the US asylum system” and deters migrants from coming to the US.

“The injunction now in effect is deeply flawed and should be stayed pending appeal and pending any further proceedings in this Court,” the filing reads.

The Trump administration has rolled out a slew of policies in recent weeks to try to curb migration to the United States amid high border apprehension numbers. The solicitor general acknowledged the uptick in illegal border crossings in Monday’s filing.

The rule, which was issued from the departments of Justice and Homeland Security in July, would prohibit migrants who have resided in or traveled through a third country from seeking asylum in the US, therefore barring migrants traveling through Mexico from being able to claim asylum. The result would be a severe limiting of who’s eligible for asylum.

Immigrant advocacy groups have claimed the rule is unlawful and leaves migrants in harm’s way.

In his July ruling, US District Judge Jon Tigar, a Barack Obama nominee, in the US District Court for the Northern District of California, wrote, “This new rule is likely invalid because it is inconsistent with the existing asylum laws.”

“An injunction,” Tigar added, “would vindicate the public’s interest – which our existing immigration laws clearly articulate – in ensuring that we do not deliver aliens into the hands of their persecutors.”

The US District Court for the Northern District of California will hold a hearing in early September.

CNN’s Geneva Sands contributed to this report.