Joe Hockey has said a meeting he had with former Helloworld executive Russell Carstensen has been misrepresented and that the allegation he “owes” Helloworld chief executive Andrew Burnes is “absolute nonsense”.

In an email to the Senate on Thursday, Carstensen said Burnes told him he was able to quickly arrange a meeting with Hockey, Australia’s ambassador in Washington, because “Hockey owes me”. Burnes denies making the statement.

Hockey is a close friend of Burnes and has a shareholding in Helloworld worth more than $1m. Burnes, a Liberal donor and the party treasurer, was also a director of Tourism Australia while Scott Morrison was managing director.

In a statement released on Friday, Hockey said his friendship with Burnes was well known and he had disclosed all his investments and shareholdings as required by the foreign affairs department before attending the meeting with Carstensen. After the meeting, he recused himself from all further engagement with the company.

His statement lays out his version of how the meeting took place.

“On 24 April, 2017 I received an email from Mr Russell Carstensen from QBT. He indicated he would be in Washington DC and would be available to visit the Embassy to discuss travel business.

“QBT and/or its associates in the Helloworld Group had been providing various travel services to the Federal Government since 2012.

“Prior to the scheduling of the meeting, I had made the Minister Counsellor (Management) and Consul General in the embassy aware of both my friendship with Mr Burnes at Helloworld and my shareholding,” he said.

“I decided to join the meeting since Helloworld/QBT was, and still is, the existing approved supplier of travel to DFAT. It is normal practice for ambassadors to meet with official suppliers of services to their department.

“The meeting was a general discussion about current arrangements for the delivery of travel services in the United States and Australia. There were no commercial opportunities with the embassy offered or available.

“After the meeting, I noted to the Minister Counsellor (Management) and Consul General in the Embassy that I wanted no further engagement with Helloworld/QBT on this matter.”

“I forwarded it to my executive assistant and heard nothing more,” he said.

“Since that time, I have excused myself from all discussions and decisions relating to the procurement of travel services.

“The US travel arrangements have since gone to tender, nearly fifteen months after the meeting in April 2017 with Mr Carstensen. The chief financial Officer of DFAT in Canberra is the decision-maker for this ongoing tender.”

Carstensen, who reported directly to Burnes, sent the email after watching the Senate estimates questioning of the finance minister, Mathias Cormann, about why he had not paid for a family trip to Singapore that was personally booked by Burnes until he was alerted by the Age and the Sydney Morning Herald.

Helloworld confirmed the failure to charge Cormann was an administrative error which meant his credit card was not billed. Cormann has subsequently paid for the trip but revealed in estimates he had booked private travel three times by calling Burnes personally.

On Wednesday it was reported that Hockey had asked embassy staff to meet company representatives.

In his email, read out by the Labor senator Penny Wong in estimates, Carstensen said he was planning to travel home from Europe on personal leave when Burnes contacted him to tell him he had arranged a meeting with Hockey and told him to fly home via Washington DC.

“I asked Mr Burnes how could this be done so quickly,” Carstensen’s email said. “He verbally advised me, ‘Hockey owes me’.”

Hockey’s statement concludes: “The allegation that I somehow ‘owe’ Mr Burnes is absolute nonsense. It is also and, most importantly, irrelevant to the conduct of the tender process run by DFAT, which I am not a party to.”