The Russian and Ukrainian foreign ministers are to hold talks on Thursday on Russia's construction of a controversial causeway which has soured relations between the two countries.
President Kuchma has visited the disputed area
Russian Foreign Minister Igor Ivanov will travel to Kiev, amid accusations Ukraine is reneging on a promise to withdraw troops from a strategic island of Tuzla in the Sea of Azov.
Ukraine has accused Russia of seeking to annex Tuzla by extending the causeway towards Ukraine's Crimean Peninsula.
Russia has denied any territorial ambitions, saying the project is intended to stop Russia's coastline eroding.
Last week, the Ukrainian parliament passed a resolution describing the Russian project as an "unfriendly act".
Ukraine has sent troops to the disputed island, which lies in the middle of the Kerch Strait, connecting the Sea of Azov with the Black Sea.
The Russian causeway stretches from the mainland towards Tuzla, and is now about 100 metres from what Kiev considers to be Ukraine's border.
Some Russian officials have cast doubt on Ukraine's claim to Tuzla, about 5.5 kilometres (3.5 miles) from the Russian mainland, to which it was connected until it was severed in a storm in 1925.
Whichever country controls Tuzla effectively controls shipping passage in the Strait, a corridor from the Sea of Azoz to Turkey and the Mediterranean.
Russia and Ukraine do not have any demarcated border in the strait.
'Bridge of friendship'
On Wednesday, the governor of Russia's Krasnodar region, Aleksandr Tkachev, said the dam should be extended to reach the Crimea.
"We are building the foundation of a new transport crossing... that should become a bridge of friendship, not a bone of contention between the two brotherly peoples," he said.
"It's not Tuzla that Ukraine needs, but the Kerch Strait."
Russian President Vladimir Putin said Mr Ivanov would take Mr Tkachev's views into account when he meets his Ukrainian counterpart Kostyantyn Hryshchenko.
Tensions eased last week when Russia agreed to suspend construction if Ukraine withdrew its troops.
But Russia has now accused Ukraine of dragging its feet.