The 32-year-old knocked out his opponent in the 10th round in the re-arranged fight at the Barclays Center to keep hold of the title he first won more than three years ago.
After claiming victory number 40 of his career, Ortiz soon turned attention to IBF and WBA champion Joshua, who is scheduled to fight WBO title holder Joseph Parker in Cardiff at the end of the month.
"I want to unify. I am ready whenever those guys are," BBC Sport quotes him as saying. "I figured out a way to come back tonight. A true champion always finds a way. That's what I did."
Joshua's promoter Eddie Hearn has previously talked up the prospect of Joshua fighting Wilder at some point in 2018, should the Brit first maintain his own unbeaten streak at the Principality Stadium on March 31.