The divisive day even swept up the presumptive nominee, Donald J. Trump. Renegade delegates forced a floor fight in an effort to embarrass him, and his top aide called Ohio’s governor “petulant” for not endorsing Mr. Trump.
The House speaker, Paul D. Ryan, who is the chairman of the convention, also distanced himself from Mr. Trump’s approach to racial unrest and from one of his signature proposals.
The unusual jousting among Republicans at their own convention gave way to more traditional, fiery speeches aimed at Democratic leaders, Mrs. Clinton and President Obama. The most impassioned remarks came from former Mayor Rudolph W. Giuliani of New York, who described an America plagued by crime and violence and repeatedly praised police officers for keeping families safe without regard to race.
“When they come to save your life, they don’t ask you if you’re black or white — they just come to save you!” Mr. Giuliani yelled.
With the overwhelmingly white audience hearing mostly from white speakers, Mr. Trump and his convention planners tapped two African-Americans to rebuke black protesters across America who have decried the fatal shootings of black men by the police.
“Ladies and gentlemen, I would like to make something very clear: Blue lives matter,” said David A. Clarke Jr., the sheriff of Milwaukee County, Wis., playing on the name of the Black Lives Matter protest movement to praise police officers. He accused protesters of contributing to anarchy and added, “So many of the actions of the Occupy movement and Black Lives Matter transcend peaceful protest and violates the code of conduct we rely on,” as the crowd erupted in cheers.
He also rubbed salt in the wounds of critics of the police by referring to the killing of Freddie Gray and saying, “There is some good news out of Baltimore, Md., as Lt. Brian Rice was acquitted on all charges.
Darryl Glenn, a black Republican from Colorado who is running for the Senate, said, “Someone with a nice tan needs to say too, ‘All lives matter.’ ”
Mr. Trump, never one to bypass the spotlight, broke with tradition twice on Monday night. He interrupted his own convention by calling in to Fox News and bragging about how he defeated John Kasich, the governor of Ohio, in the primary campaign. And later, he showed up at the convention itself, theatrically appearing in silhouette against a misty background and introducing his wife, Melania.
Ms. Trump, a Slovenian immigrant who will celebrate 10 years as an American citizen this month, delivered a glowing testimonial to what she called “the simple goodness” of her husband. Yet while she praised him in broad strokes, her speech was quickly criticized for sharing language from Michelle Obama’s speech at the 2008 Democratic convention.
The convention ran long, infuriating organizers. Senator Joni Ernst of Iowa, one of the few prominent elected Republicans speaking Monday, took the stage after 11 p.m. Eastern time, when most of the arena had emptied out.
Earlier in the day, the spectacle of open revolt on the convention floor was not just humiliating for Mr. Trump during a traditionally celebratory week. It also showed that he was struggling to pass his first important test at the convention: presenting a unified party as he begins the general election campaign against Hillary Clinton.
While Mr. Trump’s advisers insisted that Republicans would be united by the time the candidate finished speaking on Thursday night, a rump faction appeared determined to resist him and to send a message that his brand of divisive politics did not represent their party. Some delegates were already threatening to leave before Thursday, when Mr. Trump is scheduled to officially accept the party’s nomination.
He had hoped his choice of Gov. Mike Pence of Indiana as his running matewould unite the party, but affection for Mr. Pence, who drew more applause than Mr. Trump at points, has not translated into solid support for the ticket.
Mr. Trump did receive an assist from prime-time convention speakers like Patricia Smith. Her son, Sean, was killed in the 2012 attack in Benghazi, Libya, and she accused Mrs. Clinton of misleading Americans about that episode, though congressional inquiries have not found her responsible.
“I blame Hillary Clinton personally for the death of my son,” Ms. Smith said. “This entire campaign comes down to a single question: If Hillary Clinton can’t give us the truth, why should we give her the presidency?” Noticing a handmade sign in the crowd, she added, “That’s right, ‘Hillary for prison.’ She deserves to be in stripes!”
The convention is shaping up to be the most bitterly divided since 1992, when some Republicans excoriated President George Bush for raising taxes, and Patrick J. Buchanan drew applause from delegates and scowls from Bush campaign officials by declaring that “a religious war” and “cultural war” were underway for the soul of America.
As frustrated as some Republicans were with Mr. Bush, nothing back then compares to the discomfort with Mr. Trump, a brash outsider who waged a brutal primary campaign that involved insulting many of the party officials in the convention hall. Even the imperative of beating Mrs. Clinton has not proven enough for many Republican governors, members of Congress and other leaders to put aside their doubts about Mr. Trump’s temperament and preparedness and rally around him.
Against a video screen projecting “Make America Safe Again,” several speakers spent less time talking about Mr. Trump than about the needs of veterans, soldiers, police officers and Border Patrol agents.
Among the speakers were several women whose relatives were killed by people in the country illegally: killings they attributed to Mr. Obama’s immigration policies. One of them accused Mrs. Clinton of talking more about aiding “illegal aliens” and refugees, and another drew an ovation when she said Mr. Trump “cares more about Americans than illegals.”
Throughout the day, despite their exhilaration, Mr. Trump’s advisers were still focused on settling scores. In the morning, his chief adviser, Paul Manafort, unexpectedly lashed out at Mr. Kasich for refusing to support Mr. Trump after being defeated in the primaries. “He’s embarrassing his party in Ohio,” Mr. Manafort said, blaming Mr. Kasich’s chief political strategist for the lack of an endorsement.
Attacking a prominent and popular governor is unusual, especially in his home state during the party’s convention. But the Kasich camp seemed delighted to wage a battle against Mr. Trump and elevate Mr. Kasich as a cleansing candidate for the party in 2020.
Inside the hall, delegates opposed to Mr. Trump tried to use a procedural move, a demand for a roll-call vote, to delay the opening speakers and shame Mr. Trump. But they were stymied.
“Some Republicans are going through the five stages of grief over Trump, and the convention is the anger stage,” said Mike Stopa, a delegate from Massachusetts. “But I don’t think it’ll get worse. We’re Republicans. As a party, we’re not too disruptive.”
Party leaders sought to play down the split, but the divisions were palpable. The pastor who gave the afternoon benediction reminded the delegates, “Our enemy is not other Republicans, but is Hillary Clinton and the Democratic Party.”
At a lunch sponsored by The Wall Street Journal, Mr. Ryan, the House speaker, implicitly scolded Mr. Trump for his resentment-oriented appeals. “We should all kind of chill, calm down and change our tone going forward,” he said.