WASHINGTON (JTA) — U.S. Jewish leaders talk in pained, hushed tones about the “red lines” in the Turkey-Israel relationship — the ones they say the Turkish leadership has crossed and the ones they say they won’t.

The fragile consensus emerging from the establishment Jewish organizational leadership is that the relationship it has cultivated over the decades with Turkey is worth preserving — at least for now.

“There are lines that mustn’t be crossed, and we have seen over the last weeks those lines aggressively crossed,” said Jason Isaacson, the director of international affairs for the American Jewish Committee, a group that has taken a lead role over the decades in outreach to Ankara. “The dilemma is to honor the legacy of Turkey’s hospitality and integration of its Jews in its society.”

Isaacson and others referred to Turkish Prime Minister Recep Tayyip Erdogan’s likening last week of the Star of David to a swastika.

“It is going to be a challenge for them to walk back into a zone of responsibility — but they must, and we will continue to make that case very forcefully to our Turkish contacts,” Isaacson said.

The Turkey-Israel alliance reached the breaking point May 31, when Israeli commandos intercepted and boarded the Mavi Marmara, a Turkish-flagged ship that was part of a flotilla that aimed to breach Israel’s embargo of the Gaza Strip, which is controlled by the Hamas terrorist group.

Nine Turkish passengers, including one Turkish American, died in the subsequent melee. Seven Israeli soldiers were injured. Competing accounts — each backed by video outtakes — blame each side for starting the violence.

Turkey-Israel tensions have been brewing since Israel’s 2009 war in the Gaza Strip; some say they began even earlier. In 2009, Erdogan condemned Israel’s invasion of Gaza and upbraided Israeli President Shimon Peres at an economic conference in Davos, Switzerland that January. Turkish state television subsequently ran a TV series that depicted Israelis as bloodthirsty.

Daniel Pipes, who directs the Middle East Forum, says the roots of the crisis date to Erdogan’s election in 2003. Erdogan’s Islamist AKP Party is challenging the military, the redoubt of secularism in Turkey, Pipes says, and that when Israel is depicted in a negative light, the AKP weakens the military.

“It appears they no longer fear the military, and they are now are unleashing their might,” Pipes said of the AKP. “We mustn’t give up on Turkey — AKP is the problem.”

Turkey’s behavior also has taken hits from the left of the pro-Israel spectrum, which otherwise had criticized Prime Minister Benjamin Netanyahu’s government for its handling of the raid.

Turkey “has been too quick to try to make political gains for themselves at the expense of regional stability,” Jeremy Ben-Ami, who directs J Street, told JTA.

Israel’s oldest Muslim ally, Turkey in recent years has buffered the Jewish state — and Western interests — against Iranian expansionism in the region. Israeli combat pilots are able to practice drills in Turkish airspace that would not be possible over Israel’s compact territory, and Israel’s Navy counted on Turkey as an alternate harbor in case of all-out war.

In return, Turkey has benefited from the deep, broad reach of Israel’s intelligence services, particularly relating to the activities of the PKK Kurdish terrorist group. It also has relied on the American Jewish community to make its case in Washington; the Turkish Diaspora has never matched its Greek and Armenian counterparts for sustaining nationalist passions overseas.

A critical test for Turkey’s Jewish proxies in Washington has been their successful effort to quash recurring resolutions that would recognize Turkey’s Ottoman-era massacres of the Armenians as a genocide, as most experts already do. The Armenia resolution is a rare source of tension between Jewish lobbying groups, which stymie the measure to protect Israeli and U.S. interests in the region, and Jewish Congress members, who recoil at denial of a genocide.

But pro-Israel insiders, speaking off the record, say now that they are considering keeping their hands off the resolution. The version currently circulating in the U.S. House of Representatives has passed the Foreign Affairs Committee.

It stands little chance of reaching the floor, however, as long as Rep. Nancy Pelosi is the House speaker; Pelosi has closely heeded directives from the Obama and Bush White Houses to bury the resolution as long as Turkey remains a key U.S. ally in the region.

Passage would be disastrous, said Soner Cagaptay, a senior fellow at the Washington Institute for Near East Policy who tracks Turkey, as Erdogan would be able to make his Islamist, anti-Western case to the Turks with an “I told you so” argument.

“We would lose the Turks,” Cagaptay said. “And we have not lost Turkey — we have lost the steering wheel.”

Already the relationship is fraught: Turkey canceled planned joint military exercises with Israel in the wake of the flotilla raid, and on Monday it dismissed Israel’s planned query into the incident as a sham.

With the exception of the Zionist Organization of America, which has called for an investigation into Turkey’s role in the fiasco, pro-Israel groups in Washington are not willing to take commensurate leaps and directly target Turkey. Instead, they are targeting the Turkish Humanitarian Relief Foundation, or the IHH, the charity with ties to Erdogan’s AKP that helped fund the Mavi Marmara excursion.

In the House, Rep. Ron Klein (D-Fla.) wrote Secretary of State Hillary Rodham Clinton asking her to list IHH as a terrorist group because of its alleged affiliation with Hamas. Five House members from New York accepted a petition Monday demanding the same action that had been organized by the Jewish Community Relations Council of New York and garnered 20,000 signatures.

The Senate leadership of both parties is gathering signatures for a letter to President Obama asking him to consider such a designation. Placement on a terrorist list freezes a group’s U.S. assets and makes it illegal to fund-raise in the United States.

By not targeting Turkey directly, Jewish groups want to avoid antagonizing the entire Turkish political establishment; Erdogan may yet be vulnerable because of his mishandling of the important U.S. relationship, among other reasons. And there are still redoubts of friendship to Israel, in the military and Foreign Ministry.

Another factor is Turkey’s Jewish community.

“American Jews who have been longtime supporters of Turkey must keep alive the people-to-people dialogue, considering that over 20,000 Jews live in Turkey today,” said a lobbyist who has represented both Jewish and Turkish interests and still travels frequently to Turkey.

Cagaptay warned that the relationship, while worth salvaging, would never be the same.

“The days of Turkey watching Israel’s back in a tough neighborhood, and of Turkey counting on Israel to represent its interests in Washington, are over,” he said.