Dozens of nationalist protestors on Saturday stormed the headquarters of the pro-Kurdish
The protesters broke into the building where the office is located, scattering papers and furniture on the street and removing the HDP sign from the entrance, images taken by the Dogan news agency showed.
A group then ascended to the top of the building, setting off a fire and draping from the top a giant red flag with three crescent moons, the insignia of right-wing Nationalist Movement Party (MHP).
The government has said the outlawed Kurdistan Workers Party (PKK), which is fighting a bitter insurgency against the Turkish security forces in the southeast, was likely behind the attack earlier that left 13 Turkish soldiers dead.
The HDP denies any links to the PKK but the government accuses the party of being the political front of the militants. Several HDP MPs including its co-leaders are currently under arrest over alleged links to the PKK.
The HDP earlier condemned the attack on the soldiers "in the strongest possible terms".
But it added: "We have long passed the stage of settling with messages of condemnation. We all must stand together for peace, democracy, justice and freedom against violence, to end this pain."
Turkish media said that Saturday's protesters were supporters of the Grey Wolves, a militant wing of the MHP who were hugely prominent in the 1980s and 1990s.
Kayseri is seen as one of the strongholds of the nationalist party in Turkey, although the ruling Islamic-rooted Justice and Development Party (AKP) has made inroads there in recent years.
Meanwhile, angry right-wing protesters also attacked an outdoor meeting of the the opposition Republican People's Party (CHP) in central Kayseri, the Hurriyet daily said.