Ferguson's complaint asks the United States District Court for the Western District of Washington to declare unconstitutional key provisions of President Donald Trump's immigration Executive Order.
The lawyers criticized the order as "unconstitutional, un-American and unlawful".
They added they are "confident that the Executive Order will ultimately be struck down by the courts", and vowed to "work together to ensure the federal government obeys the Constitution", the statement said.
The New York attorney general used Twitter on Sunday to appeal to travelers detained at New York's JFK airport to contact his office.
Attorney General Ferguson also said the lawsuit will talk about the economic impact on the state, citing companies like Expedia and Amazon as companies who will have business and employees affected by president's order.
The executive action, which the president signed Friday, bring a 90-day ban on refugees from Iran, Iraq, Libya, Somalia, Sudan, Syria, and Yemen.
The White House has remained defiant over the travel ban, which prevents people from Iraq, Iran, Sudan, Somalia, Libya, Syria and Yemen travelling to the USA, despite several judges ruling it is "unconstitutional and unlawful". The total population from these countries exceeds 130 million.
Throughout Sunday, tens of thousands of protesters rallied before the White House, at more than 30 US airports, and in the central downtown of big cities including Boston, Philadelphia, Atlanta, Los Angeles, Seattle and Chicago.
Muslim women pray during the "Boston Protest Against Muslim Ban and Anti-Immigration Orders" protesting U.S. President Donald Trump's executive order travel ban in Boston, Massachusetts, U.S. January 29, 2017.
"Religious liberty has been, and always will be, a bedrock principle of our country and no president can change that truth".
Moreover, White House counselor Kellyanne Conway said earlier on Sunday the global travel disruptions in the wake of the ban were "a small price to pay" for the greater security of the United States.
The AG announcement comes on the heels of four federal judges - from New York, Washington, Massachusetts and Virginia - issuing orders since Saturday night to halt parts of Trump's bans.