He said frustrations and tension were being fueled by the slow pace at which the Greek authorities were processing the migrants’ asylum applications, and a sluggish European relocation program that has moved 3,700 people to other countries from Greece over the past year, far short of the target of 66,400.

If the pace does not pick up, “it will take several years to resolve the problem,” Mr. Schoenbauer said.

“This is not going to go away,” he continued, adding that economic migrants who do not merit asylum should be repatriated “in a humane and dignified way” to free up space at the camps.

More than 60,000 refugees or asylum seekers are in Greece, the vast majority in camps across the country, most of them cramped and dirty. Over 5,700 are on Lesbos, which has borne the brunt of the migrant influx into Greece.

Arrivals from neighboring Turkey have dropped since the peak of the crisis this time last year, when thousands made the short, perilous journey across the Aegean Sea aboard rickety boats, many drowning in the attempt. An agreement in March between the European Union and Turkey to curb human smuggling across the Aegean reduced the arrivals to virtually zero. However, there has been a significant uptick since July, after the failed coup attempt in Turkey. Now scores, sometimes hundreds, are arriving daily.

The increase in arrivals and rising tensions in the camps have fueled protests in some communities close to state-run camps where many residents are fed up with the growing migrant populations. Last week, residents on another Aegean island, Chios, protested. The upheaval has been exploited by members of far-right groups who have also protested, often clashing with more moderate demonstrators.

Mayor Spyros Galinos of Lesbos said the protests were being “guided by certain circles, far-right circles who are being supported by members of other parties that have found the opportunity to boost their following, and all this is a dangerous climate that can become explosive.”

Addressing a United Nations summit meeting in New York on Monday, the Greek prime minister, Alexis Tsipras, called on other European Union countries to take in more refugees from Greece and emphasized the risk of giving “space to nationalistic and xenophobic forces to show their faces.”