"The government of Mexico congratulates Fernandez on his triumph in the Argentine presidential election and reaffirms its readiness to renew the ties of friendship and cooperation that we historically enjoy", the Mexican Foreign Ministry said in a statement.
Venezuelan Foreign Minister Jorge Arreaza has called the victory of Fernandez a "triumph".
"[Venezuelan President] Nicolas Maduro congratulates the Argentine people, elected President Alberto Fernandez, and Cristina Fernandez de Kirchner [elected vice president of Argentina] on the victory in the election. This is a triumph that undoubtedly expresses the hope of the Argentine people", Arreaza wrote on Twitter.
The elected president will take office on 10 December.
The presidential election was held in Argentina on Sunday, with six candidates running in them. With 96.5 percent of ballots counted, Fernandez has 48.06 percent of the vote, while incumbent President Mauricio Macri has secured 40.4 percent.
Argentina has been in a deep economic recession for years. Persistently high inflation and growing unemployment leave some 35 percent of the population below the poverty line. In late June 2018, the International Monetary Fund (IMF) approved a $50-billion standby loan to Argentina. Then, in late October of the same year, the IMF agreed to increase the total size of the country's loan program to $56.3 billion.