Charlie Keating IV died after IS attackers overran the Kurdish Peshmerga frontline near Mosul on Tuesday morning.
The 31-year-old’s grandfather, Charles Keating, served prison time for his role in a huge savings and loan scandal in the 1980s.
The Islamic State used suicide car bombs and bulldozers to break through the Peshmerga frontline on Tuesday.
They advanced on the base where the says Keating and other Seals have been advising and assisting the Kurdish forces.
The US responded with F-15s and drones that dropped more than 20 bombs, said a US official.
Keating was a Seal based in San Diego, California.
The elite serviceman was a former Phoenix, Arizona, star distance runner who went on to join the athletics team at Indiana University.
He is the third American serviceman to die in combat in Iraq since the US-led coalition launched its campaign against the Islamic State group in the summer of 2014, according to officials.
Arizona Governor Doug Ducey ordered all state flags be lowered to half-mast on Wednesday in honor of the serviceman.
Keating had been planning to get married in November, according to his former track coach.
Rob Reniewicki said he is heartbroken by the death of his former protege.
“He was a tremendous athlete, a tremendous person,” Mr Reniewicki told Phoenix TV station KTVK.
“I’m devastated. I’m crushed. I’m trying to hold myself together.”
Arizona US Senator John McCain also paid tribute to Keating in a statement.
“Like so many brave Americans who came before him, Charlie sacrificed his life in honorable service to our nation for a cause greater than self-interest, which we can never truly repay,” Senator McCain said in a statement.
He was among five senators who were accused of impropriety in the 1980s after they took campaign donations from Keating’s grandfather while appealing to regulators on his behalf.
Senator McCain was later cleared of wrongdoing. Keating died in 2014, aged 90.
Thousands of depositors were fleeced in the $150 billion savings-and-loan crisis.