It comes as DHS Secretary Alejandro Mayorkas will be on the border Wednesday.
President Joe Biden's executive action on asylum, which was rolled out three weeks ago, has decreased encounters along the border by 40%, the Biden administration said.
The executive action established a rule to turn away migrants who are claiming asylum between ports of entry after there have been seven consecutive days of more than 2,500 encounters along the southern border.
The restrictions on asylum claims would remain in place for an additional 14 days once daily encounters at the border fall to a seven-day average of 1,500 or less.
Watch Biden's full remarks on the executive action
The American Civil Liberties Union (ACLU), the Texas Civil Rights Project and other civil rights organizations filed a federal complaint challenging the rule, saying it puts vulnerable migrants at risk.
The administration claims the new rule is having an impact, but said the rule is "no substitute" for the bipartisan border bill which failed to advance in the Senate in May.
The daily average of encounters along the border are 2,400 a day - not enough to lift the asylum restrictions but trending downward, the administration said.
The numbers come as Homeland Security Secretary Alejandro Mayorkas will be along the southwest border on Wednesday, touring operations.
Since the executive action was implemented, DHS has removed and returned more than 24,000 individuals to more than 20 countries, including by operating more than 100 international repatriation flights.