Prime Minister Binali Yildirim blamed the attack on the "killer PKK", referring to the outlawed rebel Kurdistan Workers' Party.
"We will fight them both in urban centres and rural areas with determination," he vowed.
Turkey remains on high alert after multiple attacks on its soil that have killed well over 200 people in the past year and have been blamed on, or claimed by, Kurdish militants and Islamic State (IS) jihadists.
Images carried by Turkish media showed a massive plume of black smoke rising from the rubble of the severely damaged police station in the town of Midyat near the Syrian border.
The windows of houses in the neighbourhood were shattered by the force of the blast.
Yildirim said one police officer and two civilians have been confirmed dead so far while 30 people were injured.
The police station blast comes a day after a bombing in the heart of Istanbul killed 11 people, including several police, the latest in a spate of attacks in Turkey's largest city.
The government on Wednesday put the toll at six officers and five civilians.
There was no claim of responsibility for the Istanbul bombing but President Recep Tayyip Erdogan too suggested that Kurdish militants were behind it.
Intense offensive
A radical splinter group of the PKK, the Kurdistan Freedom Falcons (TAK), claimed responsibility for two bombings in Ankara earlier this year that killed dozens of people.
Violence flared last year between Kurdish rebels and government forces, shattering a 2013 ceasefire reached after secret talks between PKK leader Abdullah Ocalan and the Turkish state.
Turkey has been waging an intense offensive against the PKK, deploying tanks in several towns in the southeast in recent months to "cleanse" them of rebel elements.
Activists have accused the security forces of causing huge destruction and killing civilians.
But the government says the operations are essential for public safety, blaming the PKK -- listed as a terror group by Ankara and its Western allies -- for the damage.
Over 40,000 people have been killed since the PKK took up arms in 1984 demanding an independent state for Kurds. Since then the group has narrowed its demands to greater autonomy and cultural rights.
NATO-member Turkey is also a member of the US-led coalition fighting the IS group, which controls large swathes of territory in neighbouring Syria and Iraq.
Ankara blames the jihadists for two suicide blasts in Istanbul this year, in which a total of 15 tourists were killed.
