The gunfight ended up with three deaths and two injuries, said Delaware State Police Sergeant Paul Shavack.
The suspected gunman and two women were dead. One female victim is suspected to be the gunman's wife.
Wilmington Mayor Dennis Williams said the gunman was killed by police.
US President Barack Obama is currently seeking public support for his package of gun control reforms.
A mass shooting at an elementary school in Connecticut in December killed 26 people including 20 schoolchildren.