By Alisha Ebrahimji and Artemis Moshtaghian, CNN

(CNN) — A migrant surge continues to overwhelm authorities at the US-Mexico border — and in US cities where many asylum seekers are being sent.

Here are the latest developments:

After attempting to pump the brakes on “rogue buses” from Texas dropping off migrants by the thousands, the mayor of New York City has filed a lawsuit against a dozen charter bus companies that transported migrants from Texas to New York City.

The lawsuit, which names 17 charter bus companies from Texas, Louisiana, Ohio and Indiana, was filed in New York Supreme Court on Wednesday and is seeking $708 million in damages to cover the care provided for at least 33,600 asylum seekers who have arrived in the city since 2022.

CNN has reached out to offices for the 17 bus companies.

Mayor Adams’ latest legal action to curb the flow of asylum seekers to New York City aims to tackle the financial burden placed on the city as a result of the mounting migrant crisis that is taxing local resources, which are already stretched thin.

Last week Adams signed an executive order requiring all charter buses carrying asylum seekers into the city to comply with guidelines that regulate when and where migrants can be dropped off, and requires advance written notice of their arrival under the threat of impound, fines and even jail time. But “not one bus from Texas” had complied, Adams’ chief counsel Lisa Zornberg said Tuesday.

At the direction of Texas’ Republican Gov. Greg Abbott, the Lone Star state has bused over 90,000 migrants to “sanctuary cities” run by Democratic elected officials like New York, Washington, DC, Chicago, Philadelphia, Denver and Los Angeles since April 2022, according to numbers released by the governor’s office Friday.

The lawsuit, filed by New York City Social Services Commissioner Molly Wasow Park, singles out 17 charter bus companies, alleging they acted in “bad faith” by intentionally transporting “people into New York with the ‘evil intention’ of shifting the costs of the care” for them to the state of New York.

From April 2022 through December 29, 2023, the bus companies transported individuals knowing that “they were transporting individuals who were likely to, and in fact did, seek shelter and emergency services from the City of New York,” the lawsuit alleges.

Abbott dismissed the lawsuit in comments he posted on the governor’s state website.

“This lawsuit is baseless and deserves to be sanctioned,” Abbott said in an online statement Thursday in response to the lawsuit. “It’s clear that Mayor Adams knows nothing about the Commerce Clause of the U.S. Constitution, or about the constitutional right to travel that has been recognized by the U.S. Supreme Court.”

“Every migrant bused or flown to New York City did so voluntarily, after having been authorized by the Biden Administration to remain in the United States,” he continued. “As such, they have constitutional authority to travel across the country that Mayor Adams is interfering with. If the Mayor persists in this lawsuit, he may be held legally accountable for his violations.”

The suit cites Section 149 of the New York Social Services Law, which says, any person “who knowingly brings, or causes to be brought, a needy person from out of the state into this state for the purpose of making him a public charge” will be obligated “to convey such person out of the state or to support him at his own expense.”

The charter bus companies “have violated state law by not paying the cost of caring for these migrants, and that’s why we are suing to recoup approximately $700 million already spent to care for migrants sent here in the last two years by Texas,” Adams said in a statement Thursday.

The lawsuit alleges the charter bus companies “have earned millions of dollars in revenues from Texas” for aiding in the implementation of Abbott’s plan to bus migrants to sanctuary cities to relieve its overwhelmed border towns.

Abbott has said the asylum seekers freely chose to go to New York, “having signed a voluntary consent waiver, available in multiple languages, upon boarding that they agreed on the destination.”

Leaders of several Chicago suburbs have also voted to restrict buses from dropping off migrants without notice.