European People's Party Group Chair Joseph Daul met leaders of conservative GERB party and right-wing Reformist Bloc, but also two parties to the left of the political spectrum.
During his visit to the Bulgarian capital on Tuesday Sofia Daul called on political parties to forge a center-right government.
Right-wing Reformist Bloc's Parliament group heads have rejected a proposal made by GERB leader Boyko Borisov that the two parties co-form a minority cabinet.
After a session of the RB's lawmakers that followed consultations of all political parties in Parliament on Tuesday, both Radan Kanev and Meglena Kuneva said their alliance was not willing to join a minority coalition.
The chairpersons of the parliamentary groups are gathering on Tuesday upon the invitation of GERB leader Boyko Borisov to discuss the setting up of Bulgaria's new government.
It is expected that they will discuss the three time frames for the next government, outlined by Borisov in his opening remarks in Parliament on Monday - by next summer, by the autumn of 2016 and a full term.
"I am ready to assume the full responsibility, though I am aware that this will be detrimental to the party," Boyko Borisov, leader of GERB - the party with largest number of seats in Parliament said at the opening session.
"However, it will be more detrimental if we don't have a government and hold new early elections in January," he added.