In a move seen in Israel as a bid to smooth ties after recent sharp differences over Israeli building in East Jerusalem, Rahm Emanuel paid a rare visit as White House chief of staff to Israel, delivering in person an invitation to Prime Minister Benjamin Netanyahu to meet with President Barack Obama next week.

Mr. Emanuel, who is combining business with a family vacation to celebrate the bar mitzvah of his son Zach, has been a lightning rod for blunt criticism because of his Jewish identity and ties to Israel. Israeli hard-liners who consider the Obama administration as hostile to the Jewish state have called him an "anti-Semite" and a "traitor."

Itamar Ben-Gvir, an parliamentary aide to a far-right Israeli legislator, said he and other pro-settler activists staked out the Western Wall plaza in the Old City of Jerusalem in hopes of demonstrating against Emanuel.

"It’s a joke to come and have a good time in Israel and then to come out against Israel," says Mr. Ben Gvir, who distributed a poster in March calling President Obama an "agent" of the Palestine Liberation Organization.

Ben Gvir blames Emanuel for the freeze on new housing in the West Bank. "He has frozen our lives in Judea and Samaria," he says, "but not only that, he wants to ruin our lives in the state of Israel."

Strong personal ties to Israel

Emanuel's father was born in Jerusalem, fought in the Irgun underground militia before Israel's establishment, and moved to the US. As a boy, Emanuel went to summer camp in Israel, and also did a stint volunteering in the Israeli army.

But those links only enhance the dismay of some Israelis that Emanuel is the right-hand man of a president they consider more sympathetic to the Palestinians than to Israel, says Akiva Eldar, a former Washington correspondent for the liberal Haaretz newspaper.

"People in the US don't understand that to Israelis, his name sounds like a kibbutznik or a war hero. So the expectations are high. And if you are not completely pro-Israeli, you’re a traitor," he says.

"His image is that he's very liberal, and that he doesn't have a problem criticizing Israel…. Regardless of his Jewish identity, he's an Obama guy. So he starts from a problematic point."

Tensions date to Clinton administration

But the bad blood may go beyond Obama to Emanuel's involvement in the administration of former President Bill Clinton, who had rocky ties with Netanyahu during his first stint as prime minister. At times of tension, Israeli newspapers have cited unnamed officials close to Prime Minister Netanyahu as singling out Emanuel as responsible, Mr. Eldar says.

Despite the tension, there has been a healthy press coverage of the Emanuel family visit, from what Emanuel ordered at a restaurant in the resort city of Eilat to his trip to an Israeli air force base.

The Obama administration and the Netanyahu government have disagreed over the expansion of Jewish settlements in the West Bank and East Jerusalem, prompting the worst open dispute in two decades.

Arik Ziv, a member of Netanyahu's Likud party who publishes an online newspaper reflecting the ideological right wing, insists that Emanuel, like many Israeli peaceniks, has an innate distaste for the prime minister.

"It’s on a personal level," he says. "Even if tomorrow [Netanyahu] makes an agreement with the Palestinians, they wouldn't like him. Rahm Emmanuel and Peace Now [an Israeli left-wing opponent of settlements] are the same thing."