The move came a day after the church said it was opposed to any compromise including the name 'Macedonia', which is also the name of a northern Greek province over which wars were fought a century ago.
"I hope you will contribute...so that Greece, in a spirit of unity and rational speech, will successfully deal with the issue...without the mistakes of the past," Tsipras wrote to the head of the Church of Greece, Archbishop Ieronymos.
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Hopes of a solution to the issue, which dates from 1991, were revived after a new government was elected in Skopje last year determined to bury the hatchet with Athens, in return for a NATO seat.
"I believe it's possible to find a solution by the end of the first semester of 2018," Macedonia Prime Minister Zoran Zaev told Greece's Alpha TV over the weekend.
Ahead of a new round of UN talks next week, Greek Foreign Minister Nikos Kotzias and his Macedonia counterpart Nikola Dimitrov met behind closed doors in Thessaloniki on Friday.
Greece and the EU recognise the small landlocked country by its provisional name, the former Yugoslav Republic of Macedonia (FYROM), under which it was also admitted to the UN.
Skopje has long insisted that this designation was only provisional.
In Greece, there is already opposition in the north of the country to any solution including the name Macedonia, and the issue may split the Greek parliament, which will be called upon to ratify any deal.
"I believe it's possible to find a solution": Macedonia Prime Minister Zoran Zaev. Source: AAP
Defence Minister Panos Kammenos, the government's nationalist coalition partner, is also opposed to such a solution.
But Kotzias this week hinted that with over 100 nations already recognising the tiny Balkan state as Macedonia, options are limited.
"The baby is 25 years old, it has already been baptised," Kotzias told Antenna TV on Monday.
"We want to add...a composite name in a way that (the country) will be distinct from Greek Macedonia," he said.
Both sides have declined to comment on speculation that New Macedonia will be the chosen compromise.
On Monday, Kotzias noted that the name Nova Makedonija is among proposals floated in the past.
