Monday's meeting confirmed "the European will to have Ukraine closer (to Europe) ... and the idea of a road map for visa liberalization," Frattini told journalists, Earth Times reported.
"We decided that with the Russian Federation, so it's logical we do it with Ukraine as well," Frattini said.
Yanukovych is set to travel to Brussels to meet top EU officials on March 1 as his first foreign visit, diplomatic sources said.
The EU's foreign-policy director, Catherine Ashton, is due to represent the bloc at his inauguration on Thursday.
Monday's move came after a number of Central and Eastern European member states pushed for the EU to offer Ukraine a path towards visa-free travel as a way of improving diplomatic ties and boosting pro-Western forces in the country.
The EU "should strengthen those in Ukraine who wish to become more European by offering Ukraine a road map towards a visa-free regime," Polish Foreign Minister Radoslaw Sikorski said.
Latvian Foreign Minister Maris Riekstins added that "We have to look first at President Yanukovych's foreign-policy priorities ... Visa liberalization is one of the issues which from my point of view is important."
Ukrainian citizens enjoyed visa-free travel to EU states such as Poland until 2007. But the EU's new members then joined the bloc's Schengen zone which abolished all passport controls between EU states - and therefore obliged them to introduce visa regimes for their non-EU neighbours.
That move was deeply resented in Ukraine.
Sikorski stressed that any visa-liberalization plan would come with strict conditions attached.
"A road map is not a guarantee. A road map only says that if you follow the road, you will arrive at the destination, but if you stop on the road you won't," he said.
Riekstins stressed that "the Ukrainians have a way to go on internal reforms" before they can hope for free travel to the EU.
Other ministers at the meeting did not comment directly on the proposal.
But Germany's deputy foreign minister, Werner Hoyer, said that Europe "needs Ukraine as a reliable partner" and that ministers must debate "how we can actively support Ukraine in its reform process."
A number of EU commentators in recent days have said that they would welcome Yanukovych's inauguration if he proved predictable and effective.
Speaking ahead of the meeting, an EU diplomat said, "If the election of Yanukovych gives clarity, stability and a leadership with whom we can have a clear relationship, so much the better."
After the Monday meeting, Ashton said that all the ministers present had called on the bloc to help Ukraine become more stable.
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