The Churches stance has since 1992 been that FYROM is "appropriating and claiming what it does not own, that is, the Greek name of Macedonia, and thus injuring the Greek dignity and the historic reality".
Tsipras told Greek state television ERT that he believes an agreement would benefit all the countries in the region, according to RFE/RL.
Many countries including Turkey recognize Macedonia with its present name.
The new government of Macedonia under Prime Minister Zoran Zaev has accelerated negotiations with Greece to solve the problem. Dimitrov met his Greek counterpart, Nikos Kotzias, on Thursday in Thessaloniki to discuss ways to move forward in the long-standing dispute.
The Foreign Ministry in Athens said after the meeting that they will continue their efforts on January 17, when they are scheduled to meet with the United Nations special envoy for the Macedonian issue, Matthew Nimetz, at UN headquarters in NY.
"What I think is important is that we have achieved substantial progress in confidence-building between the two countries that finally will result in finding a.solution of the dispute", he said.
Under a 1995 accord, Greece has only agreed that the country be referred to internationally as the Former Yugoslav Republic of Macedonia until the dispute is resolved.
Athens has blocked Macedonia's attempts to join North Atlantic Treaty Organisation and objects to its European Union membership bid because it says the name Macedonia implies a territorial claim over Greece's own northerly region of that name.
"It is a national issue that can not leave the Church of Greece indifferent", Ieronymos told the Board of the Holy Synod that was summoned last night (local time) with the participation of four Bishops from Northern Greece, all opposing to the inclusion of any term that related to the "Macedonia" name in the new FYROM title.
The Greek Orthodox Church, Greek nationalist parties, and residents of northern Greece have been especially opposed to any compromise that incorporates the name Macedonia and have planned rallies in northern Greece later this month.
Skopje insists that designation was never meant to be permanent.