Iran’s missile attack against Israel on Tuesday roiled the U.S. presidential race, pushing the White House — and Vice President Kamala Harris — to take a firmer stand on the chaos in the Middle East.

Ms. Harris was silent until later in the day, when she condemned the attack and said she backed Mr. Biden for offering U.S. assistance in shooting down nearly 200 missiles.

Mr. Biden said he was “fully, fully supportive” of Israel but declined to say what more that meant, beyond the initial assistance in defending against the attack. Asked specifically about consequences for Iran, he said that “remains to be seen.”

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Former President Donald Trump said Mr. Biden and Ms. Harris have left the U.S. rudderless and the “whole world is unraveling.”

“We have a nonexistent president and a nonexistent vice president, who should be in charge, but nobody knows what is going on,” he said at a campaign stop in Wisconsin. “No one is in charge of our country.”

Iran’s missiles were the latest escalation in the nearly year-old conflict ignited by Hamas’s grisly attack on Israel on Oct. 7. Israeli retaliation against the Palestinian terrorist group renewed violence from Hezbollah, the Iranian-backed terrorist forces in Lebanon. Israel last week killed Hezbollah’s leader, sparking Iran’s attack.

Israel was attacked a little more than a month before Election Day, and Mr. Trump and Ms. Harris were in what polls show as a tight battle for the White House.

Mr. Trump has cast his lot firmly with Israel and accused Ms. Harris of being too worried about her political left flank, some of which has turned decidedly anti-Israel. Those factions have called on her to embrace an arms embargo, which would cut off essential U.S. aid to Israel.

Ms. Harris has said she would not stop military aid, but beyond that, her silence left others to fill in the blanks.

“I assume that Vice President Harris will continue to hew closely to the administration’s position, but as much as her team will want to get her on the campaign trail to the extent possible, including fundraisers, at least for the short term, she is going to have to spend lots of time focusing on what is happening in the Middle East as well,” Jim Manley, a Democratic Party strategist, told The Washington Times.

“I don’t know if this is the October surprise everyone has been waiting for, but this has the potential to spiral out of control,” he said.

Hatem Abudayyeh, executive director of the Arab American Action Network, demanded that Ms. Harris rein in Israel. In a statement, he labeled her “Killer Kamala” and Mr. Biden “Genocide Joe.”

Sen. Lindsey Graham, South Carolina Republican, said Congress should step away from its preelection hiatus and return to Washington to approve more assistance for Israel. He said it could be combined with a hurricane relief package.

Mr. Trump has argued that, as president, he had defanged Iran by ending President Obama’s nuclear deal that sent billions of dollars to Tehran in exchange for iffy promises to halt nuclear development.

He said he left Iran “in total check.”

“Iran wants Kamala Harris to be president,” Mr. Trump said before warning that the “world will go up in smoke” if the Democrat wins.

Halie Soifer, CEO of the Jewish Democratic Council of America and a former Harris aide, blasted Mr. Trump for “unconscionable” statements.

“It also underscores that America’s national security & that of our allies, including Israel, is not Donald Trump’s priority,” she said on social media.

The Republican Jewish Coalition countered that the chaos belongs to the Democrats.

“Kamala Harris owns this mess as a vocal champion of the disastrous Iran nuclear deal, which allowed Iran to develop ballistic missiles — the same missiles used in today’s attack on Israel,” said Sam Markstein, RJC’s national political director.

• Stephen Dinan contributed to this report.