JERUSALEM — Americans living in Israel went to the polls this week, dropping sealed envelopes into improvised ballot boxes at community centers in this city and at other locations around the country.  Instead of a unifying experience, though, participating in the November presidential elections from afar seemed to accentuate the distance between the American Jewish voters here and those back in the United States.

An American Jewish Committee Survey conducted in early September showed nearly two-thirds of Jewish voters were supporting President Obama, in line with support in past elections. According to exit polls since 1992, about three-quarters of Jewish Americans have supported the Democratic presidential candidate.

Historically, the vote from Israel has hardly counted. The number of eligible American voters here is now estimated at about 160,000. In 2008, about 30,000 cast absentee ballots. Many here said the process of registering and voting was just too complicated.

But this time as many as 75,000 Americans in Israel have registered for a ballot, spurred on perhaps by the critical issues on the American-Israeli agenda but also by the efforts of iVoteIsrael, a get-out-the-vote group that says it is nonpartisan but that critics accuse of working quietly for the Republicans.

Whatever the reasons — whether the background of tensions between Prime Minister Benjamin Netanyahu and the Obama administration, the looming threat of a nuclear Iran or simply the greater turnout because of efforts by iVoteIsrael — a number of people casting their ballots at an event sponsored by the group said they supported Mitt Romney, the Republican challenger.

“In the United States, like most people, I voted Democratic,” said Dr. Naftali Neal Fish, a clinical psychologist and hypnotherapist who came to Israel from Philadelphia in the 1980s. This was his first time voting abroad. Citing both the crisis with Iran and the economic situation in the United States, where American-Israelis still pay taxes, he said he voted for Mr. Romney.

Orit Straus, an interior decorator who came here with her family three years ago from St. Louis, said she had voted for Mr. Romney “because I feel he is better for Israel.”

Meir Simchah Panzer, from Virginia, said that there was probably little substantive difference between the candidates but that he was voting for Mr. Romney “by default; I see somebody who seems genuinely to care and to have principles.”

Daniel Laufer, 26, from North Miami Beach, Fla., said he voted for Mr. Romney because of his “economic record” and because he had become “disenchanted with Obama’s Middle East policies.”

iVoteIsrael has sponsored debates around the country and reached out to potential voters through social networks, community e-mail lists and local publications. Its activists have gone door to door, run phone banks, canvassed outside shopping malls and registered parents at Little League games. It has provided drop boxes for registration forms and ballots in locations like pizzerias and private homes, including in several West Bank settlements.

It has not endorsed any candidate, and the Web site of the United States Embassy lists it as a nonpartisan group offering voter assistance. Elie Pieprz, iVoteIsrael’s national campaign director, said the group had registered voters from 49 states, including “thousands” in critical swing states like Florida and Ohio.

“While the 2000 Bush-Gore presidential elections all came down to 537 absentee ballots cast in Florida, only 64 of those — out of the many thousands of Floridian-Israelis — were cast from Israel!” the group states on its Web site, adding, “We want to see a president in the White House who will support and stand by Israel in absolute commitment to its safety, security and right to defend itself.”

But critics from the Democratic camp have noted that some of iVoteIsrael’s messaging, particularly on its Facebook page, has a distinct anti-Obama flavor, including an appeal to vote from the hawkish former United Nations ambassador, John R. Bolton, who has endorsed Mr. Romney.

Adding to the uncertainty, iVoteIsrael has also been vague about the sources of its financing. Its parent organization, Americans for Jerusalem, is a registered 501(c)(4) organization that does not have to disclose its financial backers. But the Sunlight Foundation Reporting Group said last week that Americans for Jerusalem appeared to have ties to Ronald S. Lauder, the conservative American businessman, philanthropist and supporter of Republican causes. Mr. Lauder’s office said it had no comment.

Mr. Pieprz, a former Republican activist who came to Israel in 2010, said only that iVoteIsrael was financed by supporters from the right and the left and that its day-to-day operations were run independently of Americans for Jerusalem.

The apparent growth in absentee voting has stirred a contentious debate over whether the numbers are great enough to make a difference.

“In raw numbers,” Mr. Pieprz said, “the votes from Israel can absolutely change an election.”

Republicans Abroad Israel, which represents the party here, has focused its efforts on the senatorial race in Ohio, where the Democrat, Sherrod Brown, has a healthy lead. Marc Zell, a chairman of Republicans Abroad Israel, said it had mobilized dozens of volunteers to submit opinion pieces, letters and responses to the Ohio news media in support of Josh Mandel, the Republican candidate, as well as Mr. Romney and Israel. Mr. Zell added that volunteers from Israel have also been calling potential voters in Florida.

But the idea that Americans in Israel could swing the November elections is largely dismissed by Obama supporters.

Hillel Schenker, vice chairman of Democrats Abroad Israel, said that in 2000: “Florida was stolen. I don’t think it was the absentee ballots but the manipulations.” Moreover, the skeptics note, most American-Israelis are likely to vote in states like New York, California and Illinois, where they will have zero impact.

David A. Harris, president and chief executive of the National Jewish Democratic Council, said, “I’d argue that unfortunately for the Romney-Ryan ticket, Americans living in Israel are unlikely to be the difference makers.”