Malcolm Turnbull has bowed to cabinet resistance and objections from the government’s conservative faction and declined to support Kevin Rudd for the role of secretary general of the United Nations.

Turnbull was given a captain’s call on the issue by cabinet colleagues on Thursday after ministers expressed different views about whether or not the former Labor prime minister should be nominated.

Addressing reporters in Sydney on Friday, Turnbull said he made a “considered judgment” not to back Rudd because he was not suited to the role.

“There is a fundamental threshold point, and it is this: does the government believe, do we believe, do I as prime minister believe that Mr Rudd is well suited for that role? My considered judgment is that he is not,” Turnbull told reporters.

The prime minister said he’d conveyed the reasons why to Rudd when he spoke to him on Friday morning, and didn’t want to add to the former prime minister’s disappointment by articulating them publicly.

Turnbull rejected a question about whether the rebuff for Rudd was, as its essence, a partisan one. “This decision has got nothing to do with Mr Rudd’s party, nothing at all,” he said.

The prime minister’s decision on Friday followed a lengthy cabinet discussion in Canberra on Thursday in which the treasurer, Scott Morrison, the finance minister, Mathias Cormann, and the immigration minister, Peter Dutton, spoke against Rudd’s candidacy.

Articulating the objections of the Liberal party’s conservative wing on Twitter, the South Australian Liberal senator Cory Bernardi said ahead of Turnbull’s decision: “If being former PM is reason enough to be nominated for secretary general to the UN, why don’t we nominate Tony Abbott?”

Nomination is a necessary prerequisite for Rudd’s bid, so Turnbull’s verdict essentially scuttles his campaign.

Turnbull’s decision is a direct rebuff to his deputy and key political ally, the foreign minister Julie Bishop, who supported Rudd’s candidacy.

In an effort to find a way through the internal divisions, Bishop formulated a position where the Australian government could nominate the former Labor prime minister without formally endorsing his campaign.

But ahead of Thursday’s cabinet deliberation, Turnbull publicly dismissed Bishop’s argument that a nomination was not an endorsement.

The former New Zealand Labour prime minister, Helen Clark, has considerable diplomatic resources at her disposal in her bid to be UN secretary general because John Key, the conservative prime minister, has endorsed her campaign.

Asked whether the decision to reject Rudd’s candidacy was an attempt to mollify one element of his party, the prime minister said that was a “political analysis that I reject.”

Asked why he didn’t back his deputy in a key cabinet battle, Turnbull said: “I’m not going to go into discussions in the cabinet or between ministers.”

Rudd issued a statement on Friday via Facebook saying it was a pity the government had declined to support his candidacy “as the Hawke government supported Malcolm Fraser for the post of secretary general of the Commonwealth, or the Howard government supported Gareth Evans to be head of Unesco.”

The statement said the former prime minister flew to Sydney on Friday morning “requesting a meeting with the prime minister, having sought such a meeting the previous evening”.

“On arrival in Sydney Mr Turnbull telephoned Mr Rudd, indicating there was no opportunity for a meeting. Mr Turnbull stated he would not be nominating Mr Rudd as a candidate for UN secretary general,” the Rudd statement said.

Labor has backed Rudd for the position even though many shadow ministers have chequered relationships with the former prime minister, and some have openly criticised his personality and professionalism.

The Labor rationale has been that Rudd is a suitably qualified candidate, and if there is a suitably qualified Australian candidate available for a top international post, that candidate should be supported by the Australian government ahead of any partisan considerations.

Ahead of Turnbull’s decision on Friday, the acting Labor leader Tanya Plibersek told reporters any rebuff to the former prime minister would reflect the prime minister caving to his party’s right faction, and it would be an expression of the Coalition putting their own “pettiness” ahead of the national interest.

Labor’s newly appointed spokeswoman for foreign affairs, Penny Wong, said the decision had to be “about national interest and nation first, party second and certainly petty politics a long way last.”

“What we’ve seen from this government is a pretty extraordinary approach. It’s a bizarre process,” she said.

“We have had senior cabinet ministers out trying to position the prime minister and undermine the foreign minister. We’ve got cabinet government which is apparently unable to make a decision, they’ve squibbed it,” she said. “This is really a very poor and bizarre decision making process.”