A furious Kevin Rudd has released correspondence in which he wrote that on “multiple” occasions Malcolm Turnbull – who on Friday quashed his bid to run for United Nations secretary-general – had backed his candidature.

In an blistering letter to Turnbull dated May 1 sent from New York, Rudd said they had had “many” discussions about his bid before and after Turnbull became prime minister, with Turnbull stating his support for it. Based on these “assurances”, Rudd wrote, he had informally sounded out governments around the world.

The May letter was prompted by a telephone call from Turnbull in which Turnbull indicated he was not willing to support Rudd’s candidature.

Rudd recalled in the letter that he had contacted Turnbull in September for guidance on how he should address the matter “of your previously stated support” when he met Foreign Minister Julie Bishop at the UN General Assembly.

“You in fact sent me a message on your preferred Wickr system where you stated that you and the FM were ‘as one’ in your support of my candidature.”

Rudd noted he had met Turnbull in his Parliament House office on November 11, and once again “you restated your position of support”.

“You went further to ask for a list of governments whom you would need to lobby at a prime ministerial level in the future.”

The discussion had continued in Turbull’s Sydney office on December 23, with Turnbull reiterating support, according to Rudd.

“You added that when the time came to lodge my nomination, you now wanted to take it to cabinet to avoid the perception of a ‘captain’s pick’. You also said to me that the cabinet process would not change the outcome.”

Rudd wrote that he would not have approached governments, even informally, “had you expressed any doubt about my candidature in any of our previous conversations”.

Turnbull had always said to him that the Australian government would be “mad” not to support his candidature, he wrote. “You will recall saying the same in person to me when we met at my place in New York last year.”

Rudd said that in his formal request to the government to nominate him, made in April, he had indicated the nomination needed to be lodged with the UN by early May.

“You will understand therefore how shocked I was to receive your telephone call within the last couple of hours, just prior to your taking the matter to cabinet in Canberra. In your telephone call you said that neither you nor the cabinet would be supporting my nomination. When I asked the reasons for this, you said that neither you nor the cabinet has the view that ‘I had the qualifications for the position’. You will appreciate that you have never expressed that view to me in the multiple conversations we have had on this matter in the past.”

Rudd went on to ask that Turnbull “reconsider the government’s position”, saying he had been encouraged by multiple governments from all continents to be a candidate.

According to Rudd sources, Turnbull then did not take the matter to cabinet and Bishop contacted Rudd indicating she and Turnbull had agreed it was better to have cabinet consider it post-election because that environment would be much more positive. Rudd believes Bishop has always acted in good faith.

In his letter to the Prime Minister on Thursday night – written against the background that cabinet had left the decision on Rudd’s bid to Turnbull – Rudd asked for a personal meeting to put his case “and to respectfully ask for your support”. But Turnbull refused the meeting, instead ringing Rudd on Friday morning to reject the nomination.

In his April 4 letter formally seeking nomination, Rudd told Turnbull he would hope to run “the most modest campaign structure of all candidates”. He said the government would need a single senior experienced officer, with a support officer, to co-ordinate the campaign out of New York. He would campaign personally in capitals with logistical support from missions in the field.

In this letter Rudd wrote: “Thank you for the support you have offered me in our discussions on my candidature. If I succeed, I believe I can do Australia proud.”

Turnbull’s spokeswoman on Friday night denied Turnbull had offered Rudd support when they spoke in December. “He was informed in December it was a decision for cabinet,” she said. Turnbull’s office has not yet addressed his claims about other conversations and expressions of support.