In a statement Monday, the Phoenix Police Department maintained its officers acted properly and acknowledged that the offer is just a fraction of the original $8 million negligence claim sought by Carol Ann Gotbaum's three young children.
City officials said no taxpayer money will be spent on the settlement, which still needs to be approved by a New York court.
Gotbaum, 45, was the step-daughter-in-law of outgoing New York City Public Advocate Betsy Gotbaum.
Authorities said Carol Gotbaum was intoxicated and unruly after missing her connecting flight while heading to a substance-abuse rehabilitation clinic in Tucson on Sept. 28, 2007.
After a gate agent told her that she couldn't use another passenger's boarding pass to get on a flight because of security reasons, she threw her cellphone and ran through the airport screaming she wasn't a terrorist.
Police confronted and arrested Gotbaum. But minutes after she was put in a holding cell, she died.
Authorities said Gotbaum accidentally asphyxiated herself after being chained to a bench in a police holding room and that officers didn't know she suffered from alcoholism and depression.
The Maricopa County Medical Examiner's Office ruled that Gotbaum, who was taking antidepressants, accidentally strangled herself with her shackles.