Malcolm Turnbull has prevented Kevin Rudd from running to be secretary-general of the United Nations, declaring he is not suitable for the job.

After a divided cabinet on Thursday left Turnbull to make a “captain’s call” on the nomination, Turnbull telephoned Rudd on Friday morning to tell him of his decision.

Turnbull had been under enormous pressure from the Liberal right in particular, but also wider sections of the party, to block Rudd.

The decision is a major rebuff and embarrassment for Foreign Minister Julie Bishop, who had backed the nomination and carried the argument for it in cabinet, and a victory for Treasurer Scott Morrison and Immigration Minister Peter Dutton, who had gone public with their objections.

Turnbull declined to spell out why he considered Rudd, who served as prime minister and foreign minister, to be unsuitable, although he told Rudd.

At his news conference Turnbull said the fundamental threshold point was: “Does the government believe, do we believe, do I as prime minister believe that Mr Rudd is well suited for that role? My considered judgement is that he is not.

“Not everyone is well suited for every role. This is no disparagement of Mr Rudd. He is a former prime minister of Australia. But my judgement is that he is not well suited for this particular role.” He said the decision had “nothing at all” to do with Rudd’s Labor affiliations.

Asked whether Australia would support New Zealand’s candidate, former prime minister Helen Clark, Turnbull said the government would consider what position it took on other candidates.

Conservative Liberal senator Cory Bernardi issued a statement strongly praising Turnbull, saying the decision reflected “the sentiments of a great many Australians”.

“Our participation in international institutions is more important than an individual’s ambition. While seeking to advance Australia’s stature on the world stage, we’ve got to do what’s right, rather than what’s politically expedient. The prime minister had done exactly that today.”