"The Ukrainian Constitution prohibits the deployment of military bases on Ukrainian territory - I mean military bases of foreign states," he said, speaking at the Council on Foreign Relations in New York.
He said, however, that his country would continue to seek NATO membership.
"Ukraine's NATO membership and Ukraine's independence are synonyms," he said.
He added that his country "could not be proud" of its relations with Russia. Among the main issues in bilateral relations are maritime border demarcation, Russian citizenship of many Crimean residents and the Russia's naval base in the Crimean Peninsula.
In an August 11 open letter to Yushchenko, Russian President Dmitry Medvedev blamed Kiev for the deterioration in relations between the two former Soviet republics, strained in recent years by gas disputes, Ukraine's desire to join NATO, and interpretations of the Soviet-era famine in Ukraine.
Russia has also accused Ukraine of supplying weapons to Georgia during last year's war between Russia and Georgia over South Ossetia.
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