President McAleese has extended an official invitation to the President of Russia to visit Ireland.
On the third day of her official visit to Russia, the President met with Dmitry Medvedev in the Kremlin.
The meeting was the first on Russian soil between an Irish and Russian president for over 20 years.
Among the items discussed were trade between the two countries and increasing business links particularly in the Information Technology sector.
The upcoming soccer match between Russia and Ireland was also raised and the President promised to send DVDs of Gaelic football and hurling to the Russian President.
The President also suggested that any visit by President Medvedev should coincide with a Gaelic match.
The meeting between the two lasted for 30 minutes.
The President is now in Saint Petersburg where she is due to visit the memorial to the siege of Leningrad.
Yesterday, President McAleese paid tribute to the former President of the USSR Mikhail Gorbachev, describing him as a 'man of peace'.