Another six corpses were discovered on Sunday bringing the total to 31. Turkish officials have warned that the eventual figure could exceed 100.
The discoveries came as speculation intensified that Hezbollah had links with the state.
But Mr Demirel said: "The state does not commit murders, nor does it have murders committed.
"If such crimes are committed using the state's forces, then those responsible will not escape punishment.''
There have been longstanding suspicions that Hezbollah received state support in the 1980s in its fight against the separatist Kurdish PKK rebel movement.
Nearly all Hezbollah's victims have been rival Islamic activists or PKK supporters, but it has never attacked police or other security forces.
The pro-Islamist Virtue Party and Turkey's only legal Kurdish party, the People's Democracy, have both demanded a formal investigation into whether Hezbollah has any state links.
Bodies
The discovery of the corpses comes follows a major police operation against the group. They have detained almost 150 suspected members this week.
The latest bodies were discovered in two separate graves near the Mediterranean town of Tarsus. Reports said they were naked and their hands and feet had been bound.
Other human remains have been found in the cities of Ankara, Istanbul and Konya.
Turkish newspaper reports say some of the corpses have broken bones - a possible sign of torture - and other victims had been buried alive.
Several bodies have been identified as pro-Islamic businessmen who apparently refused to support the group. Another belongs to Islamic feminist writer Konca Kuris.
Prime Minister Bulent Ecevit said many more corpses could still be found as police started searching new sites.
Mr Ecevit has already warned that Hezbollah may have infiltrated several state institutions.
On Friday, police arrested a suspected militant who was employed as a computer analyst in his office.
Some senior officials have meanwhile said they have evidence that Hezbollah militants have been trained and financed by Iran - an allegation denied in Tehran.
Gun battle
The Turkish authorities have been worried about the activities of Hezbollah for some time.
But they achieved a breakthrough last week when the group's military leader, Huseyin Velioglu, was killed in a gun battle at a house in Istanbul.
The police captured two other senior members of Hezbollah and retrieved computer discs and videos that are understood to have revealed much valuable information.
Hezbollah, which is not thought to have any connection with the Lebanese group of the same name, is committed to setting up a strict Islamic state.