"I am looking forward to the day when we will also welcome Lithuania as a member of the euro zone. But it is up to you to decide, of course," Van Rompuy said after meeting with Lithuania's President Dalia Grybauskaitė in Vilnius on Tuesday.
He said he knew that Lithuania still needed to make some progress on some of the so-called Maastricht criteria, which are prescribed for all countries aspiring to join the euro zone.
"As far as I know, on some avenues huge progress has already been made and on one or two targets additional effort is needed. But this is a decision that has to be made in the first place by Lithuanian government," Van Rompuy told journalists.
Lithuania's government has set a goal of adopting the euro in 2015.
Beware of complacency
Regardless of the improving financial situation in the euro zone, member-states of the European Union should proceed with their reforms in economic restructuring, Van Rompuy believes.
"I am confident that 2012 marked the turning point in the crisis in the euro zone. While the financial situation is improving, we should not fall into the trap of complacency," Van Rompuy said in Vilnius on Tuesday.
He emphasized that economies operated in cycles, therefore, some time had to pass after ensuring stability to economic recovery and from economic recovery to positive effects upon the labor market.
"Member-states have to continue reforming their economies. There is no alternative to that policy, there is no way back," Van Rompuy said.
He also urged member-states to move towards "a genuine economic and monetary union" by way of ensuring rapid progress towards a banking union.