The shoemaker did not address the controversy in announcing its plans for a $184 million factory with at least 500 jobs in Goodyear.
Despite his earlier criticism, Ducey welcomed Nike to Arizona on Thursday.
"This is good news for Arizona and for @GoodyearAZGov," he wrote on Twitter. "500 plus jobs. Over $184 million in capital investment. Arizona is open for business, and we welcome @Nike to our state."
Nike faced criticism last week for its decision not to sell the Nike Air Max 1 USA shoe, which included a Revolutionary-era emblem known as the Betsy Ross flag.
Former NFL quarterback Colin Kaepernick, who has a high-profile endorsement deal with Nike, told the company the flag recalls an era when black people were enslaved and that it has been appropriated by white nationalist groups, a person familiar with the conversation told The Associated Press last week.
"Arizona's economy is doing just fine without Nike," Ducey wrote on Twitter. "We don't need to suck up to companies that consciously denigrate our nation's history."
He said he's "embarrassed for Nike," called its decision "a shameful retreat" and ordered the Arizona Commerce Authority to withdraw a grant of up to $1 million.
But Nike will still get more than $2 million in tax breaks from the city of Goodyear, where Nike said it will begin work on the facility later this year and begin making soles in 2020. It will be the third U.S. manufacturing center for Nike Air.
The company, based in Beaverton, Oregon, recently expanded plants in its home state and Missouri.
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