The Helloworld chief executive, Andrew Burnes, has denied allegations he told a former employee he was able to organise a meeting with Australia’s ambassador to the US, Joe Hockey, quickly because “Hockey owes me”.

The claims were made in an email to the Senate on Thursday by Russell Carstensen, who was the group general manager of Helloworld subsidiary QBT until August last year, in which he sought to clarify his meeting with the ambassador.

Hockey is one of the top shareholders in Helloworld, with an investment worth more than $1m, and Burnes is an honorary Liberal party treasurer and donor. Burnes was also a director of Tourism Australia while Scott Morrison was managing director.

The email has fuelled a story that began when it was revealed the finance minister, Mathias Cormann, had not been charged for a family trip to Singapore that was personally booked by Burnes until he was alerted by the Age and the Sydney Morning Herald newspapers. Helloworld confirmed it was an administrative error which meant his credit card was not billed and Cormann has subsequently paid for the trip but revealed he had booked private travel by calling Burnes directly three times.

This was followed by reports on Wednesday that Hockey had asked embassy staff to meet with company representatives, a meeting that took place in Washington on 26 April 2017.

Carstensen, who reported directly to Burnes, sent the email on Thursday after watching the Senate estimates hearings. His email alleges:

Burnes told him Hockey had complained about his existing travel arrangements;

Burnes told him the Hockey meeting was arranged quickly because “Hockey owes me”;

the whole-of-Australian-government (WoAG) travel team was uncomfortable with the meeting;

people in the Department of Foreign Affairs and Trade (Dfat) were uncomfortable with the meeting;

he did not know at the time of the meeting that Hockey was a shareholder in the company.

Carstensen alleges that he was aware Burnes was going to arrange a meeting some time in the first half of 2017, but when he was returning from a personal European trip on 23 April 2017, Burnes directed him to fly via Washington for the meeting.

“[When] I asked Mr Burnes how could this be done so quickly he verbally advised me, ‘Hockey owes me’,” Carstensen wrote.

“I found that ‘owes me’ comment strange in the circumstances but it’s not an unusual term from Mr Burnes when talking about his business relationships. I knew Mr Burnes and Mrs Burnes has [sic] had a long-term friendship with Mr Hockey and his family.”

But Burnes released a statement after the estimates session, through a spokesman, which says: “I emphatically deny ever having told Mr Carstensen that Mr Hockey ‘owes me’ or any words to that effect.”

“Joe Hockey and I have been close friends for 20 years and it would be ridiculous to suggest I would say or imply he owes me anything.”

“I did not organise any meetings between Russell Carstensen and Joe Hockey. Mr Carstensen’s own email of April 24, 2017 shows that he organised the meeting with Mr Hockey and I was simply CCed on the email.”

“Further, Mr Hockey and I did not discuss the meeting in Washington at any time after it took place. DFAT employees were present at all times in that meeting and the meeting was disclosed by Mr Carstensen to the department of finance at the time, as was appropriate and necessary under the contractural arrangements”.

“Hockey owes me” - bombshell emails just released in Helloworld estimates #auspol pic.twitter.com/azdIadlRbI — Amy Remeikis (@AmyRemeikis) February 21, 2019

Late on Thursday, the trade minister, Simon Birmingham, described Carstensen as a “disgruntled former employee” and said he did not see “any allegation of impropriety”.

“Evidence all week from every public servant and official about any procurement issues is that the letter of the law and the book in terms of policy process was followed every step of the way, completely detached from any political process,” Birmingham told the ABC.

The email was revealed just an hour before the last question time as parliament rises until budget week in early April – the Coalition government’s very last parliamentary sitting week before the election.

Senior Dfat officials had been scrambling under questioning throughout the morning, with the secretary, Frances Adamson, defending Hockey’s actions, saying Hockey had rightfully declared his holdings.

However, Adamson also told Labor’s Penny Wong: “There are whole range of things you have raised today I think we need to think about and we need to provide answers to you. I’m not in a position now to say that in all respects those actions have met the standard.”

The issue dominated question time for the second day in a row as Labor unsuccessfully tried to suspend standing orders. The Labor leader, Bill Shorten, accused the Liberal party of being contemptuous with public funds.

“This is a Liberal government of their donors, by the donors, for the donors,” Shorten said.

Shorten said Helloworld would be the first item of business for Labor’s promised national integrity commission.

In his email, Carstensen said in early 2017, Burnes had allegedly told him that “his long-term friend Mr Hockey” had been frustrated with his travel arrangements because they were “unprofessional” and had “limited hours of operations”.

Carstensen said he emailed Hockey via his government email address, telling him Burnes had told him to meet the ambassador. Afterwards, he returned to Australia and debriefed Burnes.

“I advised him that the embassy business would have to go to tender but there was a [sic] excellent opportunity to get that business, especially that wanted [sic] and to hub the Americas travel out of Washington as discussed,” Carstensen wrote.

“At the time Helloworld was looking at buying a corporate business in the USA, one based in the Washington area. I told Mr Hockey this.”

Carstensen emailed Hockey when he returned to Australia and gave him corporate travel options “in detail”.

“I assume these details could have been used at a basis of the tender requirements if a tender came up,” he wrote.

When he advised the WoAG travel team that he met Hockey, “the feedback from the WoAG travel team was that they were uncomfortable with the meeting”.

“I decided then that I would not follow up with Mr Hockey. I was advised later in a conversation that ‘people’ in Dfat were uncomfortable that Mr Hockey met me and that he was a shareholder of Helloworld,” Carstensen wrote.

“If I remember correctly I did not know at the time of the meeting in Washington that he was a shareholder.”

In 2014, Cormann announced QBT as the new whole-of-government travel manager for the next four years, with responsibility for $2.1bn worth of travel expected over that period. In his statement, Cormann said QBT Pty Ltd was awarded the contract after a competitive tendering process conducted by the Department of Finance.

He said replacing the current panel arrangement with a single provider would reduce the cost of administration, but it caused controversy at the time over the potential loss of travel credits already accrued by government.

Birmingham defended the decision, saying QBT was first appointed under the previous Labor government.

“They won a contract renewal under us, but first a contract under the previous government,” Birmingham said.

“It went through a proper public procurement process, handled by the public servants who run these processes, and they managed to win the contract again.”