Thousands of illegal migrants crossed the border as President Biden's executive order restricting asylum for most illegal immigrants seemed to have no immediate impact.

In a executive action announced this week, Biden implemented an asylum ban that allows US immigration officials to quickly deport migrants who cross illegally to their home countries or to turn them back to Mexico.

Customs and Border Protection (CBP) sources told Fox News that Border Patrol apprehended about 4,000 illegal immigrants between ports of entry at the southern border on Wednesday.

This is on par or a little bit higher than what the averages have been in recent weeks, which is usually in the mid to high 3,000s or around 4,000.

Immigrant advocates criticized Biden's announcement, saying it mirrored hardline actions of former President Donald Trump as the two are facing a rematch in the presidential election later this year.

The American Civil Liberties Union said it planned to sue over Biden's measures.

US asylum law requires proof of persecution due to race, religion, nationality, membership in a particular social group, or political opinion, with cases usually decided by an immigration judge.

Biden's new policy raises the bar for initial asylum screenings for migrants which could lead to more claims being rejected sooner, or some people being denied outright if they fail to express fear of return.

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Democrats raised concerns that the move was a return to Trump-era policies.

Representative for Washington Pramila Jayapal said: "This attempt to shut down the border to asylum seekers uses the same section of US immigration laws that convicted felon Donald Trump used to implement the Muslim Ban and in attempts to cut off all access to asylum.

"While there are some differences from Trump’s actions, the reality is that this utilizes the same failed enforcement-only approach, penalizes asylum seekers, and furthers a false narrative that these actions will 'fix' the border."

Meanwhile, Republicans said the move was too little, too late, and conservative commentators pointed to the new ICE guidance as proof it lacked teeth.

Head of the Heritage Foundation’s Border Security and Immigration Center Lora Ries said: "It's bad enough that smugglers and taxpayer-funded NGOs coach illegal aliens on how to get released into the country, but now CBP and ICE are being instructed to coach them, too.

"Biden has defrauded the American people and our entire immigration system."