Mike Pence accepted his party's nomination on Wednesday night at the Republican convention, but the potential vice-president was upstaged by Texas Senator Ted Cruz, who declined to endorse Donald Trump.

Cruz finished second in the delegate count to Trump but it didn't translate into an endorsement for the Republican presidential nominee, leading to some boos in the crowded Cleveland arena on night three of the party's convention.

Cruz resisted vocal pleas from the New York delegation to endorse Trump. He acknowledged their "enthusiasm," but did not deviate from his script.

"Vote for candidates up and down the ticket who you trust to defend our freedom and to be faithful to the Constitution," he said.

Cruz no doubt sought to position himself favourably for the 2020 race should Trump lose in November. A Yahoo! News report hours before his speech suggested Cruz would challenge Trump in a primary contest even if Hillary Clinton is defeated in November.

But his stance likely didn't burnish his reputation with some top Republicans.

"It was an awful, selfish speech," New Jersey Gov. Chris Christie, a Trump supporter, told MSNBC from the convention floor.

Neither Cruz nor Florida Senator Marco Rubio endorsed Trump outright after their bitter losses to the businessman in the primaries this spring, with Trump frequently using the derisive nicknames "Little Marco" and "Lyin' Ted." Trump also mocked Cruz's wife, Heidi, in a widely criticized post on Twitter.

Rubio addressed the crowd at Quicken Loans Arena via video, focusing on Clinton's response to the deaths of four Americans in Benghazi while she was secretary of state, including the U.S. Ambassador to Libya.

"It's time to fight for a new direction for America. It's time to win in November," Rubio said.

'We like Mike!'

For his part, Pence was essentially introducing himself to a national audience. He spoke of growing up surrounded by cornfields and lovingly praised his wife of 31 years, Karen, and their three children.

Pence was officially announced as part of the ticket on July 16, and he and Trump made a much-talked about appearance on 60 Minutes, where some of their perceived policy differences were highlighted by the show.

"I never thought I'd be standing here," Pence admitted after accepting the nomination for vice-president.

'Change will be huge': Pence channels Trump0:37

Pence, 57, has been a divisive figure as Indiana's governor, expressing staunch pro-life and religious freedom beliefs.

But he won over the assembled, with chants of "We Like Mike!" by the end of his speech.

"If you know anything about Hoosiers you know we love to suit up and compete," he said, referring to his state's nickname. "We play to win. That's why I joined this campaign in a heartbeat."

He turned from his personal story to advocating Trump's outsider status and leadership skills as necessary, branding Clinton as the "secretary of the status quo."

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Republicans frame election in stark terms

Scott Walker, who dropped out of the race in September 2015, was the first of the former presidential hopefuls to speak on Wednesday night.

Walker's speech, with the repeated mantra of "America deserves better," struck familiar thematic ground - that Democrats aren't doing enough to support the military and police, or to keep Americans safe from attack.

"We believe in a country where we take the threat of terrorism seriously," said Walker. "You know the words: Radical. Islamic. Terrorism."

Florida Gov. Rick Scott, the first speaker on the night, continued the stark framing of the upcoming presidential election seen over the previous two nights.

"This election is about the very survival of the American Dream," said Scott.

The "lock her up" chant continued — referring to Clinton and her perceived crimes — during the speeches of Scott and conservative talk show host Laura Ingraham. The chant had been heard earlier in the week, particularly in a heated mock prosecution given by Christie.

Donald Trump-Ivanka

Trump gives two thumbs up as Donald Trump Jr., left, and Ivanka Trump, right, stand and cheer for Eric Trump as he delivers his speech on Wednesday night. (Joe Raedle/Getty Images)

Ralph Alvarado, a state senator from Kentucky, sought Wednesday to broaden the tent for Trump as several polls suggested Clinton has a huge advantage with respect to prospective Hispanic voters.

Alvarado wove a hard-working immigrant tale, his parents coming to the U.S. from Costa Rica and Argentina.

"At their core, Hispanics believe what Republicans believe — traditional family values, church, faith and God, the dignity of work and the opportunity for self-sufficiency that comes from a free society and limited government," said Alvarado.

Daytime arrests outside venue

Following a well-received speech by his brother Donald Jr. a night earlier, Eric Trump continued the familial theme, going on immediately following the divisive Cruz speech.

"Vote for the one candidate who does not need this job," he said in support of his father.

Newt Gingrich also took to the stage. The former Speaker of the U.S. House of Representatives and 2012 Republican presidential candidate had campaigned to be Trump's running mate but lost out to Pence, Indiana's governor.

Gingrich said it was vital that the next president not "sleepwalk through history" on the matter of security, while prefacing his remarks with the belief that the vast majority of Muslims are peaceful and would make ideal neighbours.

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Supporters of the Revolutionary Communist Party, U.S.A., burn the American flag outside the gates of the Quicken Loans Arena on Wednesday. (Adrees Latif/Reuters)

"The challenge is when even a small percentage of a billion, six hundred million people support violence against those that disagree with them, that is still a giant recruiting base," said Gingrich.

Outside the venue Wednesday afternoon, police fired pepper spray at a surging crowd and took several people into custody as skirmishes broke.

A Cleveland police official said about a dozen were taken into custody and would be charged.

Police said two officers were assaulted and suffered minor injuries.

Carl Dix, a representative of Revolutionary Communist Party, said the group organized the burning of the American flag as a "political statement about the crimes of the American empire. There's nothing great about America."

with files from The Associated Press