"For once, you could perhaps be concerned about the PKK, a terrorist organization on the EU list, which brutally executed 13 people in Gara, Iraq. Or would that get you into trouble with the PKK lobby?" Turkish presidential spokesman Ibrahim Kalin said in a post on his Twitter account on Wednesday.
The remarks came after the spokesperson for EU foreign affairs and security policy, Peter Stano, issued a statement on Turkey's recent actions against some members of the HDP.
"The European Union is gravely concerned about the continuing pressure against the HDP and several of its members, which has materialized lately through arrests, replacing elected mayors, what seem to be politically-motivated judicial proceedings and the attempt of lifting parliamentary immunities of Members of the Grand National Assembly," the statement said.
On February 14, Turkish officials said PKK militants had executed over a dozen kidnapped Turks, including military and police personnel, in a cave in northern Iraq.
Turkish police detained 718 people in 40 cities over alleged links to the Kurdish militants it blamed for the executions.
The Turkish Interior Ministry said heads of the HDP in cities and districts were among those detained.
The PKK said the 13 men had died when Turkish forces bombed the cave where the captives were being held.
Stano further stressed that any alleged wrongdoing or crime needed to be subject to due process and that the presumption of innocence must be safeguarded.
The HDP is Turkey's second-largest opposition party after the Republican People's Party (CHP).
The Turkish government has long accused the HDP of having links to the PKK, which is listed as a terrorist group by Turkey, the US, and the EU.
In recent years, Ankara has jailed dozens of mayors and other officials from the HDP. The party denies having any links with the separatist militants.
The PKK has for decades used Iraq's mountainous areas as a springboard for attacks on Turkish troops.
PKK militants also regularly clash with Turkish forces in the Kurdish-dominated southeast of Turkey attached to northern Iraq.
The militant group has been seeking an autonomous Kurdish region since 1984.
More than 40,000 people have been killed in the decades-long conflict between Turkey and the Kurdish militant group.
A shaky ceasefire between the PKK and the Turkish government collapsed in July 2015. Attacks on Turkish security forces have increased since then.