"America must remain open to people of all faiths & backgrounds", Albright wrote.
Mr. Trump's argument, as stated on the campaign trail prior to his Election Day victory, is that not all refugees from unsafe regions want liberty as laid out by the Declaration of Independence and codified into law by the U.S. Constitution.
Albright is not alone in her public proclamation that she would register as Muslim in protest.
Environmentalists are 'out of control': Trump to auto execs
Mr Marchionne told reporters after the meeting that the president did not give them specifics on what regulations he would cut. Also on Tuesday, Toyota said it would add 400 jobs and invest $600m in an in plant, aiming to boost production there by 10%.
Executive orders expected to be signed by Mr. Trump related to immigration and border security have prompted Ms. Albright to join a "solidarity" movement championed last weekend by the Women's March on Washington.
Albright, who served under President Bill Clinton, didn't elaborate on where or how she would register as a Muslim. "I stand ready to register as a Muslim in #solidarity if it comes to that".
Albright herself came to the U.S.as a child after her family fled Nazi persecution in Europe, so this is an issue close to her heart. Instead, he said he wanted to negotiate with countries individually. Democratic House Leader Nancy Pelosi also stated that, with those executive actions, "the president is turning his back on both our history and our values as a proud nation of immigrants".
Trump is traveling to Philadelphia to address Republican lawmakers gathered for a party retreat. But the planes are only considered to be Air Force One when the president is on board.