Former UN head Kofi Annan is among leading politicians attending talks in San Sebastián which could bring about the dissolution of ETA.
The armed Basque separatist group has killed more than 800 people over four decades, but has been weakened by arrests over recent years and is currently observing a ceasefire, which it declared in January of this year.
Former Irish Prime Minister Bertie Ahern and Sinn Fein president Gerry Adams will also be attending the conference in northern Spain, with the intention of sharing their experience of ending the Northern Irish conflict.
Jonathan Powell, who was closely involved in those negotiations as chief of staff to former British Prime Minister Tony Blair, is also attending the conference.
Spain's government has continued to call on ETA to disarm and dissolve and ETA's political wing has already committed to a peaceful struggle for independence.
The conference in San Sebastián will be attended by local politicians - including the Basque branch of the governing Socialist party - as well as radical Basque nationalists. They are expected to ask the terrorist organisation for a "definitive" end to its violence and for the Spanish government to negotiate.
Patxi Lopez, the Socialist leader of the Basque regional parliament, urged ETA and its supporters to "to take advantage of this opportunity, to truly take advantage to put a final end to it".
The Spanish government has refused to engage with ETA, saying it will not negotiate while the group remains armed. Spain's conservative opposition party, the PP - which is expected to win a general election next month - has also refused to attend the conference. Both have pointed to ETA's "permanent ceasefire" declared in March 2006, which was broken nine months later when a bomb was planted at Madrid airport, killing two people.