Some disappointed gift-givers had instead handed the gifts to presidential staff, Ayariga said.
War on corruption
Mills took office in January, pledging a "relentless war" against corruption.
However, his present-snubbing has not been appreciated by everyone.
James Agbagana, a traditional chief, warned that the president was going too far and that he could ruin the Ghanaian tradition of hospitality.
Vitus Azeem, the head of Ghana Integrity Initiative, the local chapter of Transparency International, said the president's actions would do little to stem corruption among fellow government officials.
"His campaign would have been more meaningful if he had given out specific directives to his ministers and other top officials to also turn away the hampers and the goats driven to their homes and offices," said Azeem.