President Trump’s executive order banning travel from six predominantly Muslim countries faced a new front of opposition from the states on Thursday, as the attorney general of Washington announced that he would seek to block the order from taking effect next week.

Backed by several fellow Democratic attorneys general, Bob Ferguson of Washington said he would ask a federal district judge, James Robart, to extend an order freezing the first version of Mr. Trump’s travel ban and apply it to the updated restrictions the White House unveiled on Monday.

In a news conference on Thursday, Mr. Ferguson acknowledged that Mr. Trump’s updated order was less sweeping than its predecessor. But he argued that the travel restrictions remained “effectively a Muslim ban,” with many of the same legal weaknesses as the first version.

“It’s fair to say that the revised executive order does narrow the scope of who’s impacted by it in an adverse way,” Mr. Ferguson said. “But that does not mean it has cured its constitutional problems.”