"The European Union does not support any separatist agenda for the Kurds - being it in Turkey, being it in Iraq, being it in Syria," Mogherini said at the European Parliament in Brussels on Tuesday.
Mogherini reiterated the EU's condemnation of violence by the PKK following an attack in Ankara that killed 29 people last week.
"The European Union condemns in any possible way any terrorist act and considers the PKK as a terrorist organization," Mogherini said.
"We also believe, as united as we are in condemning terrorist acts, that the way to solve the Kurdish issue inside Turkey is through a peace process that the same Turkish government started a few years ago before dropping it," she said.
What is commonly known in Turkey as the “solution process” aimed to end the 30-year conflict between Turkey and the PKK, considered a terrorist organization by Turkey, the EU and the U.S. It began in 2013 but stalled after renewed violence broke out last year.
"We continue to think this is the way and we say this to the Turkish authorities and to the Kurds equally," Mogherini said.
Mogherini said the crisis will not be solved unless the rights of Kurds are respected.
"We need to make sure that rights are respected by the Kurds and to the Kurds. Most of all, it cannot be possible to make as if this was not an issue in the region - it is," she said.