President Joe Biden warned on July 14 of the the risks of political violence in the U.S. after Saturday’s attempted assassination of former President Donald Trump, saying, “It’s time to cool it down.”

In a prime-time national address from the Oval Office, Mr. Biden said political passions can run high but “we must never descend into violence.”

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“There is no place in America for this kind of violence — for any violence. Ever. Period. No exception. We can’t allow this violence to be normalized,” Mr. Biden said.

Mr. Biden spoke for about five minutes from the Oval Office. He noted that the Republican National Convention was opening in Milwaukee on Monday, while he himself would be traveling the country to campaign for re-election.

He said passions would run high on both sides and the stakes of the election were enormous.

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“We can do this,” Mr. Biden implored, saying the nation was founded on a democracy that gave reason and balance a chance to prevail over brute force. “American democracy — where arguments are made in good faith. American democracy — where the rule of law is respected. Where decency, dignity, fair play aren’t just quaint notions, they’re living, breathing realities.”

Earlier Sunday, Mr. Biden condemned the attempted assassination of his predecessor, Trump, as “contrary to everything we stand for as a nation” and said he was ordering an independent security review of how such an attack could have happened.

He called for the country to “unite as one nation,” promised a “thorough and swift” review and asked the public not to “make assumptions” about the shooter’s motives or affiliations.

The President said he has also directed the U.S. Secret Service to review all security measures for the RNC. Hours later, Audrey Gibson-Cicchino, the Secret Service’s coordinator for the convention, said the weekend attack against Trump did not prompt any changes to the agency’s security plan for the event and officials “are fully prepared.”

In his remarks, Mr. Biden called the attack on Trump “not who we are as a nation.”

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“It’s not American. And we cannot allow this to happen,” he said. “Unity is the most elusive goal of all, but nothing is more important than that right now.”

The president said he and first lady Jill Biden were praying for the family of Corey Comperatore, a former fire chief who was shot and killed during the Trump rally Saturday night in Butler, Pennsylvania.

“He was protecting his family from the bullets,” Biden said. “God love him.”

The President also said he’d had a “short but good conversation” with Trump in the hours after the shootings and said he was “sincerely grateful” that the former president is “doing well and recovering.”

Trump, who has called for national resilience since the shooting, posted on his social media account after Biden’s remarks, “UNITE AMERICA!”

Actually achieving unity will be far more challenging, especially in the midst of a bitter presidential campaign. Biden’s team is grappling with how to calibrate the path forward after the weekend attack on the very person he is trying to defeat in November’s election.

Mr. Biden, who has set out to brand Trump as a dire threat to democracy and the nation’s very founding principles, put a temporary pause on such political messaging. Shortly after Saturday night’s attack, Biden’s reelection campaign froze “all outbound communications” and was working to pull down its television ads.

The President also postponed a planned trip to Texas on Monday, where he was to speak on the 60th anniversary of the Civil Rights Act at the Lyndon B. Johnson presidential library. An NBC News interview between Biden and anchor Lester Holt will now occur at the White House, instead of in Texas, as initially planned.

Mr. Biden’s campaign said that, after the NBC interview airs on Monday night, it and the Democratic National Committee “will continue drawing the contrast” with Trump over the course of the GOP convention — even though it remains unclear when ads would resume.

Mr. Biden also still plans to make a planned trip to Las Vegas, which will include a campaign event Wednesday. Vice President Kamala Harris postponed her planned campaign trip to Florida on Tuesday, where she had been set to meet with Republican women.

Trump, meanwhile, announced he was moving up plans to go to Milwaukee and the Republican convention, where criticism of Biden and the Democrats is sure to be searing.

The weekend developments were only the latest upheaval in a campaign that has been extraordinarily topsy-turvy in recent weeks.

Mr. Biden’s shaky debate performance on June 27 so spooked his own party that some top surrogates and donors turned on him, and nearly 20 Democratic members of Congress called on the president to leave the race outright. Facing mounting questions about whether he was fit for a second term, Biden and his top advisers have been scrambling to salvage his campaign by adding events around the country and more aggressively criticizing Trump.

Saturday’s attack upended — at least for now — that counteroffensive on the cusp of the Republican convention.

The campaign also hopes that Sunday’s Oval Office address lets Biden further drive home his point about unity while demonstrating leadership that could assuage nervous critics within his own party.

“We’ll debate and we’ll disagree, that’s not going to change,” Biden said in his afternoon remarks. “But we’ll not lose sight of who we are as Americans.”

Although investigators are still in the early stages of determining what occurred and why, some Biden critics are calling out the president for telling donors in a private call Monday that “it’s time to put Trump in the bullseye.”

A person familiar with those remarks said the president was trying to make the point that Trump had gotten away with a light public schedule after last month’s debate while the president himself faced intense scrutiny. The person spoke on the condition of anonymity to more freely discuss private conversations.

In the donor call, Mr. Biden said: “I have one job and that’s to beat Donald Trump. … I’m absolutely certain I’m the best person to be able to do that.”

He continued: “So, we’re done talking about the debate. It’s time to put Trump in the bullseye. He’s gotten away with doing nothing for the last 10 days except ride around in his golf cart, bragging about scores he didn’t score. … Anyway I won’t get into his golf game.”