The ministry has also expressed its protest against the decision of the island's leadership to build a port that could potentially compete with the port in the Argentine province of Tierra del Fuego, Argentine broadcaster TN reported.
Argentine Foreign Minister Diana Mondino has not been present during the ministry's conversation with Hayes, the report said.
Cameron visited the islands in February. Mondino later expressed concern about his trip to the disputed territory on the sidelines of the meeting of the G20 foreign ministers' meeting in Rio de Janeiro.
The Falkland Islands, or the Malvinas, remain the subject of a long-standing dispute between Argentina and the United Kingdom. In 1982, a war broke out between the countries. It lasted several weeks and ended with the defeat of the Latin American country.
In March 2013, the islands held a referendum on the status of the territory, with 99.8% of local residents having preferred to remain a UK overseas territory. Argentina has not recognized the voting results. Tensions over the territory intensified in 2015, after British oil companies discovered new oil and gas deposits near the islands.