The Texas Senator only went as far as congratulating Donald Trump who had been his bitter rival in the primary contests.
Angry chants of “We want Trump!” and “Endorse Trump!” grew louder as Ted Cruz came to the end of his speech.
Indiana Gov. Mike Pence then took centre stage to give his vice-presidential acceptance speech.
Mike Pence praised Donald Trump’s record as a businessman and said the country had “but one choice” in November.
“It’s change versus the status quo, and when Donald Trump is president, the change will be huge,” he said.
Ted Cruz is likely to steal the headlines after stoking the rage of the convention, to such an extent that his wife Heidi had to be escorted from the floor.
In his speech, Ted Cruz told supporters to “vote [with] their conscience” and not to stay at home for the general election.
Ted Cruz finished second to Donald Trump in the delegate count during a campaign that featured personal attacks by the New York tycoon on Cruz’s wife and father.
The boos that drowned him out stopped when Donald Trump entered the convention hall before Ted Cruz had finished speaking.
Donald Trump later said he knew Ted Cruz would not endorse him but had let him speak anyway.
New Jersey Gov. Chris Christie said his actions were “awful” and New York Congressman Peter King called the speech “disgraceful”.
The drama came at the end of the day when the Republicans tried to finally put the plagiarism scandal behind them.
Melania Trump faced accusations of copying after it was discovered that lines in her remarks matched almost word for word a convention speech delivered by Michelle Obama in 2008.
After initial denials from the campaign, Meredith McIver, a Trump Organization employee, admitted her role in writing the speech and apologized for the “chaos I have caused”.
Thursday night is the main event of the four-day event – Donald Trump’s acceptance speech.
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