The survey also found that 80% of Afghans surveyed said a political solution was the only way to bring an end to fighting.
The mayor said U.S. Army Spc. Miguel Villalon's death was "personal" to him.
The Taliban control nearly half of Afghanistan, and continue to stage near-daily attacks targeting Afghan and U.S. forces.
Washington has been calling on the militants to reduce violence, posing it as a condition for resuming negotiations.
Two more soldiers were wounded in the blast.
According to the State Department, nearly 13,000 Special Immigrant Visas have been granted to Afghan nationals since 2014.
Sgt. 1st Class Michael J. Goble was killed Monday in a roadside bombing in northern Kunduz province.
The latest fatality brings the number of U.S. deaths in Afghanistan this year to 20.
Milley said the sacrifices had kept the Taliban and other insurgent groups at bay and prevented another "9/11" attack.
Good news came on Sunday afternoon when a police sergeant called the family to say they'd found the stolen pickup.