Texas Senator Ted Cruz pointedly withheld an endorsement of his formal rival and Republican nominee Donald Trump during his speech at the Republican National Convention and was booed and cheered as a result.

The two men engaged in a bitter and personal primary campaign, in which Trump insulted Cruz's wife's looks and suggested the Texan's father was with John F. Kennedy's assassin just before the president was shot.

During the campaign, Cruz called the New York real estate developer a "serial philanderer" and a "narcissist."

Cruz briefly congratulated Trump on formally securing the nomination, but did not feature Trump in his remarks after that.

Instead he focused on a critique of Democratic nominee Hillary Clinton and the Obama administration in which she served as Secretary of State.

While not endorsing Trump, Cruz did encourage Americans go to out and vote in the November presidential elections.

"We deserve leaders who stand for principle. Unite us all behind shared values. Cast aside anger for love. That is the standard we should expect, from everybody. And to those listening, please, don't stay home in November. Stand, and speak, and vote your conscience, vote for candidates up and down the ticket who you trust to defend our freedom and to be faithful to the Constitution," said Cruz.

But Cruz's comments were badly received by some in the audience who booed and chanted "Trump!"

Trump arrived in the arena at the end of Cruz's speech to attend the remarks of his son Eric.

Cruz withdrew from the primary race in May, 2016 and has hinted at a possible run in 2020.