Pol Lt Col Chamnong Wongkunannya, an officer from Thammasala police station, said villagers living in Soi Phutthamonthon Sai 2 found the first grenade on open ground about 30m from the concrete wall of Mr Suthep's house. The land is earmarked to made into a parking lot for a tour-bus company.
Security guards from Mr Suthep's house used two car tyres to cover the grenade.
Shortly afterwards the second M79 grenade head was found on an earth embankment about 30m from the location of the first device.
The two M79 rounds had apparently been fired from a spot nearby but did not explode.
Explosive ordnance disposal police were later dispatched to examine the scene.
Villagers said they believed the M79 grenades were fired from an elevated bridge about 400m away.