(CNN) Immigration advocates who filed a federal lawsuit against the Trump administration's asylum ban are waiting for the court's first move, which is expected on Tuesday.

President Donald Trump on Friday signed a proclamation setting into motion a ban on most asylum claims for immigrants who cross the US-Mexico border illegally. The proclamation put into effect a new administration rule submitted to the federal registry Thursday that serves as the legal vehicle for the ban.

Before the ban even became operational Saturday morning, the American Civil Liberties Union, Southern Poverty Law Center and Center for Constitutional Rights sued the administration on behalf of various asylum and refugee assistance groups.

The parties accused the administration in their lawsuit of "violating Congress's clear command that manner of entry cannot constitute a categorical asylum bar," as well as violating the Administrative Procedure Act by not providing public notice or comment on the rule.

"The asylum ban is flatly unlawful and will put people's lives in danger. The President has no authority to simply discard a law Congress passed," ACLU lead attorney Lee Gelernt told CNN on Monday.

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