As the struggle for the Republican nomination is beginning to heat up in an increasingly crowded field, the party's candidates are not holding back when it comes to criticising leaders of the last two election cycles.

Days after Rand Paul referred to John McCain – his Arizona Senate colleague and the GOP's 2008 nominee – as a "lapdog" for President Barack Obama's foreign policy, frontrunner Jeb Bush took a shot at Mitt Romney, who in 2012 failed to win back the White House.

The former Massachusetts governor was unable to connect with voters in a genuine way, Bush charged, according to Fox News.

"He made (the election) about a referendum on the president's policies rather than about himself," the brother of former President George W. Bush noted. "He didn't show his heart; he didn't send a signal that he cared about people, when he did."

The former Florida governor was speaking at a private Q&A with students at the Ramaz School, where he was marking the celebration of Israel's independence day. If Republicans were to choose him as their nominee, they could expect a different kind of campaign, Bush seemed to suggest.

"A lot of it is just connecting on a human level with people, not being behind some protective shield," he said.

"Campaigning in a way where you're outside your own comfort zone. Taking questions, not having it all scripted out, not having it all part of some narrative that producers made. Be more spontaneous."

His remarks about Romney paled in comparison to Paul's charge that McCain and the latter's friend and Senate ally, South Carolina's Lindsey Graham, "have been wrong about every foreign-policy issue over the last two decades."

The Kentucky senator's comments prompted an angry reaction from McCain on Wednesday, when the Arizonan said that Paul was the worst of the score of Republicans running for the White House, the New York Daily News recalled.

"The record is very clear that he simply does not have an understanding about the needs and the threats of United States national security," McCain said about Paul.

"In 2007, he said it would be ridiculous to call Iran a threat to the United States' national security. Last summer, he publicly doubted whether ISIS was a threat to the United States' national security."