The seven-state lawsuit asks Seattle's U.S. District Court Judge James Robart - who blocked the first iteration of Trump's travel ban in February - to "extend his ruling to cover parts of the president's revised directive", according to Politico. Following the legal challenges from several states and the protests that swept the country, the White House wrote a revised version of the ban, taking Iraq off the list and carving out exemptions for visa holders.
"Cutting some illegal aspects of President Trump's original travel ban does not cure his affront to our Constitution".
Since then, other states have vowed to step in, including New York, Oregon and Washington, which was the state that initially challenged the first order as well. The states may also try to go to the Supreme Court if their new challenges falter.
Federal judges struck down the first order mainly because it banned foreigners who already had legal permanent residence (known as a green card) or valid visas to enter the country.
Trump's executive order temporarily restricting immigration from six Muslim-majority countries - Iran, Libya, Somalia, Sudan, Syria and Yemen - is scheduled to go into effect on Thursday.
The first version of the order, which Trump signed on January 27, triggered howls of protest at home and overseas as well as chaos at USA airports as people were detained upon arrival and either held for hours or sent back to where they came from.
Trump on Monday signed a revised executive order to reinstate a ban on travel and immigration from six Muslim countries. Capers' office had been tasked with defending Trump's first travel ban in a NY court - an assignment he punted down to his civil division chief.
Washington Attorney General Bob Ferguson on Monday filed an amended complaint against President Donald Trump's newest travel ban, and is asking a federal judge to hear the matter on Tuesday.
The question that is being asked now is: will this action be held up, or will another federal judge have a case to suspend this one as well?
Under the new order, the refugee program would be suspended for 120 days.
But critics say the order essentially remains a ban on Muslims and therefore unconstitutional as it singles out people of a certain religion for discriminatory treatment.
One of the issues discussed at the Ninth Circuit was standing, and whether Washington state suffered harm as a result of the ban.
The restraining order does not block the entire travel ban, it simply prevents Mr Trump's administration from enforcing it against this specific family.
And hours after the man filed his complaint in Madison, Judge William Conley, chief judge of the federal court in Wisconsin's western district, issued a temporary restraining order barring enforcement against the family.
The experts said the revised order would "jeopardize our relationships with allies and partners on whom we rely for vital counter-terrorism cooperation and information-sharing".
The complaint alleges the president's travel order will harm California "by reducing investment and industry in California and decreasing travel by students, scholars, and tourists".