The first incident took place in Qalat town, 160 kilometres (100 miles) south of Quetta, the capital of restive oil and gas rich Balochistan province which borders Iran and Afghanistan.
"Three men riding a motorcycle intercepted the three tankers, threw petrol and set them on fire," local police official Lal Jan told AFP.
In the second incident, two men torched another Nato oil tanker in Mastung district, 40 kilometres south of Quetta and fled, Jan added.
A senior provincial government official Saeed Umrani also confirmed the incident and said there was no loss of life in the two incidents.
Gunmen also attacked a vehicle loaded with NATO supplies in Wadh town, 370 kilometres south of Quetta and opened fire after the driver refused to stop, wounding him and his assistant, a local police official told AFP.
The latest incidents came days after gunmen set ablaze 16 Nato oil tankers in the southwestern Dera Murad Jamali town.
Nato tankers are regularly targeted with arson attacks blamed on insurgents attempting to disrupt two key supply lines that cross Pakistan's western border bound for foreign troops fighting in neighbouring Afghanistan.
In October, gunmen torched 29 oil tankers also bound for Afghanistan in the remote Mitri area, 180 kilometres southeast of Quetta.
Balochistan is torn by militancy, sectarian violence between majority Sunnis and minority Shiite Muslims, and a separatist insurgency by rebels seeking political autonomy and a greater share of profits from natural resources.
Most supplies and equipment required by foreign troops in Afghanistan are shipped through Pakistan, although US troops increasingly use alternative routes through central Asia.
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