Greek Finance Minister Yannis Stournaras told Greece’s Parliament in a speech that negotiations had been beneficial to Greece, which had “succeeded in lengthening” the time the country had to get its fiscal house in order. Reuters

The cost of managing the migrant crisis in Greece will exceed a previous estimate of 600 million euros ($670 million) as more and more refugees are forced to remain in the country, Bank of Greece Gov. Yannis Stournaras said Sunday.

More than 41,000 refugees and migrants are stranded in Greece, their plans to travel north blocked by border shutdowns throughout the Balkans.

Just last month, a central bank source estimated 600 million euros would cover rescue operations, shelters and repatriation.

"That estimate was based on the presumption that Greece was only a transit nation, but if now we have to host a large number of refugees, this estimate will have to be revised," Stournaras told Italy's Il Sole 24 Ore newspaper.

The Organisation for Economic Cooperation and Development said last week that Greece would need help to deal with the strain that migrants were putting on its economy.

Greece also expects to talk about debt relief at the spring meeting of the International Monetary Fund in April, Stournaras said.

Athens has pledged to cut pension spending by 1 percent of GDP this year and reach a primary surplus of 3.5 percent by 2018. Stournaras said Greece's eurozone partners had promised debt relief in a meeting last year if Greece met its obligations.

"This promise has not yet been fulfilled," the central banker said. "We hope our partners and the IMF are able to fulfill the promise because it was not only a promise, but an agreement."

Eurozone finance ministers acknowledged last week that a debate on debt relief was coming up soon but said Greece should first implement pension and tax reforms, set up an independent revenue agency and deal with nonperforming loans.