More than 100 local, state and federal law enforcement officers searched 1,100 rural acres near Bogart on Friday where Zinkhan's Jeep Liberty was found pushed into a ravine late Thursday night, but the search yielded no other signs of Zinkhan.
Police said Sunday they're continuing to monitor the entire city, including the tract near the Jackson-Clarke county line where the Jeep was found and Zinkhan's West Athens house, although they no longer think he's in town.
"We cannot afford to let our guard down," Athens-Clarke police Capt. Clarence Holeman said.
After the massive daylong search Friday and a smaller search Saturday, authorities are confident Zinkhan is not in the area where his Jeep was found, and won't conduct another large-scale search unless they learn something new that leads them to believe he's hanging around, Holeman said.
Authorities continue to receive tips, said John Bankhead, a spokesman for the Georgia Bureau of Investigation, but he said Sunday he was not aware of any new leads.
Zinkhan, who had a ticket to fly Saturday to Amsterdam, where he taught part time, did not appear at Hartsfield-Jackson Atlanta International Airport to use the ticket.
The former University of Georgia marketing professor's passport is missing, but Holeman said authorities have no reason to believe he's fled the country. Federal officials say security guards at airports are on the lookout anyway.
Police say Zinkhan opened fire with two handguns April 25 at an early-afternoon reunion of the Town & Gown Players, killing three people associated with the local theater group: his wife, Marie Bruce, Tom Tanner and Ben Teague.
He then drove to a neighbor's house and dropped off his children, and he hasn't been seen since, according to police.
Zinkhan, 57, is 6-foot-3 and weighs 240 pounds. He has blue eyes and, when last seen, he had thinning gray-brown hair and a bushy goatee, although he may have shaved his facial hair and changed his hairstyle or dyed his hair.