NICOSIA, Cyprus—Cyprus wants the European Union’s border agency Frontex to step in and prevent the flow of illegal immigrant arrivals from Turkey that authorities say have stretched the eastern Mediterranean island nation’s asylum system to its limits. It’s also asking the EU to “activate all available mechanisms” to help the country manage the arrival of Syrians either directly from Syria—especially the port of Tartus—or from Lebanon or Turkey. The Cypriot Foreign Ministry says Turkey hasn’t included Cyprus in its program to halt illegal immigrant flows into the 27-member bloc since the deal was signed five years ago. The country of around 1.1 million people is also asking the EU’s executive arm to help relocate a “significant number” of Syrian asylum-seekers who have been granted international protection. “Their numbers have reached such levels that their integration into local communities is realistically unsustainable,” the ministry told The Associated Press on Thursday. According …