Ducey said he wanted state agencies to increase enforcement and public awareness of the problem. He also ordered that a planned pilot program involving new technology be accelerated and broadened.
Arizona Department of Transportation officials said last week that the pilot program would be installed beginning in the fall and that it would use thermal camera technology to notify wrong-way drivers, surrounding drivers and law enforcement.
"I want those cameras implemented as quickly as possible, and expanded to as many areas as possible where they may make a difference and save a life," Ducey said in a statement.
Drivers traveling against traffic on Arizona freeways claimed at least seven lives in 2016 and at least six so far this year, including the two people killed Tuesday night.
As of last week, the state Department of Public Safety has received at least 698 calls reporting wrong-way drivers and made at least 36 related DUI arrests this year.
The Department of Transportation in 2015 began installing hundreds of larger and lower "wrong way" and "do not enter" signs on more than 100 freeway ramps.
About 65 percent of wrong-way drivers are impaired, according to a 2015 ADOT report that also said the crashes occur most often after dark and predominantly in the morning hours from midnight to 2 a.m.
The DPS says wrong-way drivers often are between the ages of 16 and 35.
A 2012 study by the National Transportation Safety Board concluded that most wrong-way accidents occur in lanes closest to the median -- the fast lane.