One of the main topics of the talks was the question of Cyprus, which Tuomioja said would be the "most demanding" problem during Finland's six-month slot at the helm of the 25-member bloc.
The island of Cyprus has been divided into a Greek Cypriot south, representing the internationally recognized government, and a Turkish-occupied north since 1974 when Turkey invaded following an abortive Athens-backed coup of supporters of union with Greece.
In separate referenda in 2004, a U.N. plan to reunify the war-divided island was rejected by Greek Cypriots, while Turkish Cypriots approved it. President Tassos Papadopoulos was widely blamed by the international community for the 'No' vote.
On Sunday, Greek Cypriots backed parties in Papadopoulos' governing coalition in a parliamentary election, widely seen as further endorsement of the president's rejection of the U.N. reunification plan.
Bakoyannis reiterated that the Cyprus issue has to be settled by the world body, the AP reports.
The foreign ministers also discussed the EU's troubled constitution, enlargement and Finland's plans to pursue an initiative of increasing cooperation between the bloc and Russia.
Bakoyannis was scheduled to return to Athens after the one-day visit.
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