Argentine President Cristina Fernandez de Kirchner hosted President Michael D Higgins at the government mansion as part of Mr Higgins' two-week South American tour.
The President began his Latin American trip in Chile, where he met President Sebastian Pinera.
He then travelled to Brazil to meet President Dilma Rousseff and her predecessor, Luiz Inacio Lula da Silva.
Talks with the South American leaders have centred on boosting trade and tourism to Ireland.
In between meetings with heads of state, President Higgins visited members of the Irish diaspora to pay tribute to Irish immigrants.
He has also presented papers criticising unregulated trade.
As a demonstration of the two countries' historic ties, Mrs Kirchner gave Mr Higgins jerseys from local football clubs named in honour of Admiral Guillermo Brown, the first Irish-born, nationalised Argentine admiral in Argentina's navy.