By Maria Spiliopoulou

ATHENS, May 17 (Xinhua) -- Greece and Estonia support the EU enlargement on condition that candidate states will align with the international and European law, the two countries' presidents said in Athens on Thursday.

"Greece is in favor of the European perspective of the Balkan countries that are not yet member states of the EU and NATO," Greek President Prokopis Pavlopoulos said, welcoming at the presidential mansion his Estonian counterpart Kersti Kaljulaid at the start of her two-day official visit to Greece.

"However, it is obvious that this requires on their part full compliance with the international law and European Union acquis. Moreover these countries need to first resolve any differences with other EU and NATO member states," Pavlopoulos said, pointing to cases like the Former Yugoslav Republic of Macedonia (FYROM), according to an e-mailed press release from the Greek Presidency.

Greece and FYROM are at odds since FYROM declared independence from Yugoslavia in 1991 and chose the name Macedonia, which is also the name of a northern Greek province.

Athens is worried that the use of the same name by the neighboring state could lead to territorial claims.

In recent months, UN-mediated talks to resolve the issue have intensified. On Thursday after talks in Sofia on the sidelines of sidelines of the EU-Western Balkans Summit, the prime ministers of the two countries said that progress has been made.

"Estonia is a strong supporter of the EU enlargement. We have always thought that the bus doors should not close and the bus should not go away without accepting those who are ready to share our common values," Kaljulaid said on her part during statements broadcast by Greek national broadcaster ERT.

"For us it is indeed extremely important that on every step on the way we always respect common agreements and international law... We have agreed that countries can join the EU when the conditions are fulfilled," she said.

On the common challenge of the refugee crisis, both presidents stressed the necessity to embrace people in need and share the burdens.

"We need to demonstrate solidarity not only because it is a fundamental principle of our civilization, but because it is a complete rule of the European law. I would like to stress that Estonia and Greece have fully complied with their obligations ... But there are some partners who have not complied," Pavlopoulos noted.

"We fully support the reform of the EU asylum policy...We stand with you in the quest of not giving up on our continuous progress towards achieving the goals of having a clear system," the Estonian president said.

"Estonia is also the highest per capita contributor of the staff to Frontex (the European Border and Coast Guard Agency) within the whole European Union," she added, expressing her country's intention to continue cooperating with Greece in the management of the refugee crisis.

Greece has been at the forefront of the refugee and migrant crisis since 2015. More than one million people landed on Greek shores until the closure of the Balkan route to central Europe in the winter of 2016.

After the March 2016 EU-Turkey agreement aimed to stem the flows, the number of new arrivals dropped sharply. More than 60,000 people remain stranded across Greece, according to official Greek Migration Policy ministry statistics.