They had sped through a police check post barrier at Behrampur in Gurdaspur district after cops signalled them to stop, police said.
When police chased them, they abandoned their vehicle at Makhanpur village in Pathankot after covering a distance of 15 km from Behrampur in Gurdaspur, they said.
The SUV was robbed by the suspects from Sambha in Jammu yesterday, police said.
The search operation in districts of Pathankot and Gurdaspur, involving around 300 cops, lasted for about eight hours, they said.
Pathankot police searched two villages-Makhanpur and Barmal Jattan, while cops in Gurdaspur conducted search operations in around five villages along Ravi river.
"The search was also conducted in Gujjar area," Gurdaspur SSP Bhupinderjit Singh said.
Nothing suspicious was found from the SUV, police said, adding it has been seized. However, the vehicle had a fake registration number, they said.
To a query, Pathankot SSP said the three men were not dressed in army or police fatigues, as was the case with terrorists in the 2015 Gurdaspur attack.
Notably, Punjab had witnessed two terror attacks in 2015 and 2016.
In the first attack, three heavily-armed terrorists wearing army fatigues, had stormed a police station in Dinanagar town of Gurdaspur district in July 2015 killing seven persons, including a Superintendent of Police, before they were gunned down during a day-long operation.
In the second attack, four terrorists who had sneaked in from across the border, attacked the Pathankot air base on the intervening night of January 1 and 2 last year, claiming the lives of seven security personnel.