Mr Parker said it appeared the minister also misled officials by refusing to have a $4 million payment described as "compensation" because it would mean that "lawyers and bureaucrats" would become involved.
"Mr McCully deliberately misrepresented the nature of his payments to the Al-Khalaf Group so that they would not be questioned by Cabinet, the Auditor General or Treasury. His actions were deceptive."
The Green Party has also asked the Auditor General to investigate the payments.
The Saudi farm - Timeline of a deal
• In 2003, publicity around the treatment of live-sheep exports led to a voluntary moratorium.
• In 2007, the Labour Government banned the export of live animals for slaughter.
• In 2009, Agriculture Minister David Carter began negotiations with Saudi Arabia for a resumption of live-sheep exports.
• In 2010, the National Government extended the ban.
• February 2013, the Cabinet approved a proposal by Foreign Minister Murray McCully to pay $4 million to Mr Hmood Al Khalaf's business to secure it to run an agri-hub to promote New Zealand agriculture in Saudi Arabia and as a settlement of a long-running dispute over the ban on live-sheep exports, and $6 million to be paid to NZ businesses to deliver their services and help set-up the Saudi farm.
The Government also paid $1.5 million for 900 pregnant Awassi breeding ewes of Mr Al Khalaf's to be flown to the Saudi farm.
• May, 2015, after media reports on the deal, Mr McCully's office releases Cabinet papers that reveal the full cost of the deal, including the $4 million "facilitation payment" to Mr Al Khalaf. Previously, only the $6 million figure had been released.
• June, 2015, it is confirmed that lambs born on the Saudi farm suffered an extremely high death rate. The Government initially said a sand storm could be to blame, before Brownrigg Agriculture - a Hawkes Bay company that advocated on behalf of Mr Al Khalaf and later won a tender to set-up the farm - pointed to heavy rain and illnesses.
• August, 2015, Labour Export Growth and Trade spokesman David Parker writes formal complaints to the Auditor-General and Treasury Secretary, asking them to investigate whether Mr McCully and Mfat misled them over the scandal.