Slovakia, one of the EU countries that has been most critical of a pan-European approach to the migration crisis, promises that later this year it will try to help the bloc reach a goal that has so far proven elusive: a "sustainable" policy for dealing with refugees.

That claim, made Thursday by Slovakia's state secretary for European affairs, may come as a surprise given the country's reaction to some of the EU's recent migration moves, including taking the Union to court to fight a mandatory mechanism for relocating asylum-seekers, and also considering some of the rhetoric of its prime minister, Robert Fico, who has said that Muslims are "impossible to integrate" in Europe.

But the Slovaks say they can be honest brokers in finding agreement among EU countries on what has proved to be a divisive issue.

“We are fully aware of the very difficult situation,” said Ivan Korcok in a breakfast meeting with reporters, promising that Slovakia would work “to overcome fragmentation” — Brussels jargon for deep disagreements among member countries — “and deliver results.”

The country of 5.5 million people will take over the EU's rotating, six-month Council presidency from July, meaning its government will help set the Union's political agenda and its ministers will chair key decision-making meetings in the second half of 2016. It will be the first time Slovakia has held the presidency since it joined the EU in 2004.

Its job was already going to be challenging given the ongoing migration issue, but it could prove especially tough if the EU finds itself dealing with a British exit from the bloc after the country votes on its membership in a June 23 referendum.

As he laid out Bratislava's priorities, Korcok sought to allay concerns about how Slovakia would handle its time at the EU helm given its opposition to some of Brussels policies. He said he didn't "share the view of an East-West divide” on refugee policy, and said that the EU needed “sustainable migration with sustainable asylum policy.”

The man Slovak diplomats refer to as "Mr. Presidency" did not get into details of what exactly reaching “a sustainable migration policy” means, apart from implying that the current one is not manageable. But he said “there is a chance that we will have an important agreement on smart borders,” referring to the Commission proposal for ensuring tighter control of those migrants enter the Schengen area with a visa.

Korcok also said he was aware of concerns from some diplomats who say that it would be difficult during the country's presidency to make progress on the migration reforms unveiled last week by the Commission, which includes a proposal to penalize countries financially for refusing to accept relocated asylum-seekers. “The discussion about that obviously will be difficult,” he said.

He did not address concerns raised about Fico’s health. Last month the 51-year-old prime minister was hospitalized for heart surgery and has had to cancel several diplomatic visits.

But he added that Bratislava hoped “not to be fully engaged and consumed by migration” during its presidency, and to focus on other areas, including advancing policies related to finance and economics, the digital single market and energy union. He also said the Slovak presidency would push to complete negotiations with Washington on an EU-U.S. trade deal, TTIP, before the end of the Obama administration.

But Brexit will provide the first hot-potato issue for Slovakia. The country is even holding back a detailed announcement of its policy priorities until after the June 23 U.K. vote, because its outcome will determine whether diplomats have to spend the next six months refereeing EU-U.K. divorce proceedings or, in the case of an In vote, implementing reforms Brussels agreed with British Minister David Cameron as the condition of continued U.K. membership.

He added that Slovakia, as “very much a pro-enlargement country,” was in favor of Britain staying in the Union — and of helping the EU to add even more members. He said Bratislava hoped to ensure that candidate countries — including Serbia and Montenegro — “clearly make progress” toward joining the Union during the Slovak presidency.

“We see our role as a country that will make it clear to the Council and the European institutions that enlargement is extremely important and should not be neglected,” he said.