Ukraine threatened last week to refuse to allow the Russian vessels to return to the Sevastopol naval base in the Crimea, which Moscow leases from Kiev.
"We have received notification that they will return," Yuriy Yekhanurov said of the Russian ships. "We do not have any specific questions, and we will provide all the documents for them to enter" the bay of Sevastopol.
"When they will return is their own business," the minister added.
Ukrainian President Viktor Yushchenko signed a decree last Wednesday stating that Russia was required to notify the Ukrainian authorities of all movements by naval vessels and aircraft from its Crimea-based Black Sea Fleet.
Yushchenko signed the document after returning from Tbilisi, where he took part in a mass rally in support of Georgian President Mikheil Saakashvili amid fighting with Russia. Both leaders have pursued pro-Western policies, seeking to join NATO and the European Union and reduce Russian influence.
Ships from Russia's Black Sea Fleet patrolled the waters off the Georgian coast during Russia's "peace enforcement" operation that began after Georgia launched an offensive in breakaway South Ossetia on August 8. Russia's Defense Ministry said its navy had sunk a Georgian vessel transporting missile launchers.
Last Friday Yushchenko said he had presented Russia with "an urgent proposition to launch talks and draw up an agreement to regulate bilateral relations during military operations" such as those in Georgia over the past week.
Russian President Dmitry Medvedev said Monday that Moscow was ready to negotiate with Ukraine on the use of the Russian Black Sea Fleet, but would not let Kiev dictate terms. "We will be acting in line with international agreements and directives issued by me as commander-in-chief," he said.
Russia's Black Sea Fleet uses the Sevastopol base under agreements signed in 1997. Yushchenko announced earlier this year that Ukraine would not extend the lease beyond 2017.