Protests and arrests on college campuses exploded into the forefront of the presidential race this week, opening up a new line of attack for Republicans and forcing President Biden to directly address an issue that has divided the liberal wing of his party.

With Donald J. Trump largely stuck in a New York City courtroom for one of his criminal trials, Republicans have tried to use the protests as a political cudgel and a literal backdrop to attack Mr. Biden, casting him as weak and unable to keep control of the country.

For weeks, the White House has largely resisted wading into the fray, steering clear of the protests engulfing campuses over Israel’s war in Gaza. Never one to be swept up in student movements, Mr. Biden had left any comments about the rapidly evolving situation to press officers, for the most part. His White House conducted no public outreach to university administrators or to protesting students.

But as clashes on some campuses became increasingly destructive and arrests mounted across the country, Mr. Biden increased the distance between himself and some of the more radical activism on campuses. In remarks on Thursday, he struck a balance between defending free speech and describing what he saw as the limits of acceptable protest.

“Dissent is essential to democracy,” Mr. Biden said in brief comments at the White House. “But dissent must never lead to disorder or to denying the rights of others so students can finish the semester and their college education.”

The scope of the statement was limited. The president made clear he had no plans to change his Middle East policy because of the protests. When asked whether the National Guard should intervene, he quickly responded, “No.” And he did not address concerns some progressives have raised about whether the police used excessive force against demonstrators.

Biden campaign advisers believe the issue is unlikely to significantly harm the president in the election. The situation in Gaza remains highly fluid, as U.S. officials continue working toward a cease-fire deal between Hamas and Israel, and may not carry the same political resonance when voters head to the polls in November. Students are leaving campus for summer break in the coming weeks, which many believe will help defuse some of the intensity of the protests.

None of that stopped Republicans from pouncing on Mr. Biden’s comments. They accused the president of being unwilling to take stronger actions to quell the continued unrest.

“President Biden *still* won’t forcefully condemn the Hamas mobs on campuses,” Senator Tom Cotton, a Republican from Arkansas, said in a statement on social media on Thursday that cast the protesters as supporting a group considered a terrorist organization by the U.S. and many of its allies. “A complete lack of leadership from an impotent president.”

Mr. Trump’s campaign has been even more direct in placing blame on Mr. Biden. “This is Biden’s campus chaos,” read the text in one Instagram post distributed by the former president’s account that included footage of Mr. Biden defending the rights of protesters who demonstrated at some of his events.

The White House denied that the president felt political pressure to comment on the protests.

“When it comes to something like this, he doesn’t need to follow anyone or follow someone else,” the White House press secretary, Karine Jean-Pierre, told reporters traveling on Air Force One with the president. “We’ve been really consistent, I believe, in stating that when it comes to violence, violence is not protected.”

As the protests have spread on colleges across the country, Mr. Biden has been most forceful when it comes to denouncing antisemitism on campus. On Tuesday, he will deliver the keynote address at an annual ceremony hosted by the United States Holocaust Memorial Museum.

Critics in both parties have urged the administration to do more. And at times, the back-and-forth over the issue within the Democratic Party has grown bitterly contentious.

Last week, Representative Jared Moskowitz, a Democrat from Florida, suggested Senator Bernie Sanders of Vermont was evading addressing an increase in antisemitic episodes by focusing on legislation that would end military aid to Israel.

Representative Alexandria Ocasio-Cortez, a Democrat from New York, fired back by accusing Mr. Moskowitz of “shameful” treatment of Mr. Sanders, whom she noted had family killed in the Holocaust.

“My family was also killed in the Holocaust. In Germany and in Poland. My grandmother was in the kinder-transport. They also instilled values in me,” replied Mr. Moskowitz. “It’s why I voted for aid to Israel and for aid to Gaza.”

Still, some Democrats have warned that the campus unrest could depress enthusiasm for Mr. Biden among young voters. Already, polls have shown Mr. Biden struggling to retain the same level of support he received from younger voters in 2020.

On Wednesday, the College Democrats of America, the student arm of the party, offered a warning to the Biden campaign on social media.

“College Democrats’ votes are not to be taken for granted by the Democratic Party,” the group said. “We reserve the right to criticize our party when it fails to listen to us.”

Even among young voters, the issue of Israel’s war in Gaza ranks below other concerns, including the economy, abortion rights and health care. Polling conducted by the Institute of Politics at the Harvard Kennedy School last month found that “Israel/Palestine” ranked 15th in the list of concerns for voters aged 18 to 29, below not only inflation and housing, but climate change, free speech and protecting democracy.

The Republican strategy echoes efforts by Mr. Trump during the 2020 campaign, when protests over racial justice spread across the country after the killing of George Floyd by police officers.

Mr. Trump back then suggested Mr. Biden was tolerant of “Anarchists, Thugs & Agitators.” His campaign spent millions on ads in swing states, falsely attacking Mr. Biden for supporting defunding police departments.

In response, Mr. Biden forcefully condemned the violence that occasionally erupted. “Ask yourself: Do I look like a radical socialist with a soft spot for rioters?” Mr. Biden said at a speech in Pittsburgh in August 2020. “Really? I want a safe America.”

Exit polling later found that only 11 percent of voters named crime and public safety as the most important issue, far fewer than listed the pandemic, the economy and racial inequality.

Of course, there are stark differences between the protests in 2020 and those that have roiled college campuses this spring. The racial justice protests focused on a domestic issue, racial inequality and policing, while those over Palestinian rights are aimed at a conflict thousands of miles away. With as many as 26 million people estimated to have participated in demonstrations, the Black Lives Matter movement reached far beyond the campuses that have been most affected by pro-Palestinian protests.

Still, those campuses are a key source of votes for Democrats, who typically perform stronger among younger voters than their Republican rivals.

Later this month, Mr. Biden is scheduled to deliver the commencement address at Morehouse College, a historically Black university in Atlanta. Already, university administrators are facing pressure to rescind the invitation from faculty members, students and alumni.

“Any college or university that gives its commencement stage to President Biden in this moment is endorsing genocide,” wrote a group of anonymous faculty and staff in an unsigned public letter. “The time is now for Morehouse College to get on the right side of history.”