It is, of course, as much about politics as sport, a novel arena in the Palestinians’ broader campaign to leverage membership in international institutions to punish Israel and build their sovereign state. Israel argues that soccer should be a bridge for coexistence, not a diplomatic weapon: Prime Minister Benjamin Netanyahu warned Tuesday that “the thing that could destroy the football association is politicizing it.”

Mr. Netanyahu’s statement came as he met with Sepp Blatter, FIFA’s president, who on Tuesday set off on the well-trod path of shuttle diplomacy, promising to bring a message from the Israelis to his Wednesday session with President Mahmoud Abbas of the Palestinian Authority and other officials here in Ramallah.

Mr. Blatter, whose four terms as FIFA’s chief have been marred by controversy, is trying to broker a compromise to avoid a contentious vote at the congress, where a Jordanian prince is among those challenging his re-election. He declined to say what, if anything, the Israelis had offered as possible concessions or compromises, but said Mr. Netanyahu had accepted his invitation to host a “match of peace” between the Israeli and Palestinian national teams in Switzerland.

“I am here on a mission of peace,” he said at an evening news conference in Jerusalem, where a FIFA emblem proclaiming “My game is fair play” sat on the dais. “This situation cannot continue.” Noting that “there are a lot of countries in the world where there is a political conflict,” Mr. Blatter added, “There is no end to this.”

A FIFA suspension would mean that Israel’s national team would be barred from international competitions, including the World Cup and European championships, and that its professional clubs could not participate in lucrative competitions like the Champions League in Europe.