DEARBORN, Michigan (Reuters) - Widespread anger among Arab Americans and Muslims over U.S. support for Israel's wars in Gaza and Lebanon could cost Vice President Kamala Harris, the Democratic nominee, the election, Green Party candidate Jill Stein told Reuters on Sunday.

Polls show Stein garnering just 1% in the Nov. 5 election, while Harris and her Republican rival, former President Donald Trump, are almost tied with 49% and 48%.

But Stein has seen growing support among Arab Americans and Muslims in battleground states like Michigan, Arizona and Wisconsin where they have large populations that helped propel President Joe Biden to victory in the 2020 election.

"The Democrats have lost the Muslim American and the Arab American vote," Stein told Reuters after a rally attended by about 100 people in the Detroit suburb of Dearborn.

"They're going to be losing enough swing states that they will not win and they cannot win."

A Cook Political Report poll conducted from Sept. 19-25 showed Harris leading or tied with Trump in nearly all seven states that could decide the election - Michigan, Wisconsin, Pennsylvania, Arizona, Nevada, Georgia and North Carolina.

But Stein, who has been campaigning on a permanent ceasefire in Gaza and an immediate U.S. arms embargo on Israel, won 40% of the Muslim vote in Michigan in an August poll by the Council on American Islamic Relations, that also put her ahead of Harris and Trump among Muslims in Arizona and Wisconsin.

Democrats could win back those voters if they demanded and work to enact an immediate ceasefire in Gaza and Lebanon, and also halted arms sales to Israel, but there was no sign of such action, she said.

The Biden administration, along with several U.S. allies like France, has called for an immediate 21-day ceasefire across the Israel-Lebanon border and has long expressed support for a ceasefire in Gaza, but agreements have been elusive.

Asked about her potential function as a "spoiler", Stein said another Trump presidency would be "terrible" but so would four more years of Democratic rule, given high rental costs, the wars in Gaza and Lebanon, and attacks on civil liberties.

"This is a very dire situation that will be continued under both Democrats and Republicans. So we say there is no lesser evil in this race," she said.

Harris has increased her outreach in recent days, meeting with a small group of Arab American and Muslim leaders in Flint, Michigan, on Friday, and dispatching her running mate, Minnesota Governor Tim Walz, to take part in a Muslim Zoom call.

Farah Khan, co-chair of the Abandon Harris campaign in Michigan, said she would vote for a third-party candidate. "We are trying to ... punish Harris," she said. "We may not be in a large (enough) number to put somebody in office, but we are definitely in the numbers to take somebody out of the office."

Trump is also wooing Arab and Muslim voters and his campaign opened an office on Saturday in Hamtramck, a Detroit suburb whose Yemeni-American mayor Amer Ghalib has endorsed Trump.

Stein said Harris was also losing support among some union workers, Black men and Latinos, many of whom had drifted away from their traditional support for the Democratic party.

"Working people feel abandoned and betrayed by the Democratic Party," she said. "It's not like the Republicans are making things good for working people, but because the Democrats make promises and betray them, they seem to be punished by their traditional base," she said. "That train has left the station."

(Reporting by Andrea Shalal, additional reporting by Omar Younis; Editing by Michael Perry)

By Andrea Shalal