Ukraine's defence ministry has said there has been a gradual withdrawal of Russian troops from its border that may be linked to Washington's latest push for a diplomatic solution to the worst East-West crisis since the Cold War.

Oleksiy Dmytrashkivskiy, Ukraine's defence ministry spokesman, said on Monday that he could not confirm how many soldiers the drawdown involved or the number of troops still stationed at Russia's border with its former Soviet satellite.

"In recent days, the Russian forces have been gradually withdrawing from the border," Dmytrashkivskiy told the AFP news agency.

This could be linked to a regular rotation of soldiers or it may be linked to the Russian-US negotiations. Oleksiy Dmytrashkivskiy, Ukraine defence ministry spokesman,

US and EU officials estimated over the weekend that Russia's sudden military buildup along Ukraine's eastern frontier had reached between 30,000 and 40,000 soldiers.

Kiev's Centre for Military and Political Studies analyst Dmytro Tymchuk said on Monday that his sources had told him that Russia had only 10,000 soldiers remaining near the border by Monday morning.

The Ukrainian defence ministry official said Kiev had not been formally notified of the drawdown by Moscow and therefore did not know precisely why the troops were being moved.

"This could be linked to a regular rotation of soldiers," said Dmytrashkivskiy. "Or it may be linked to the Russian-US negotiations."

US Secretary of State John Kerry met Russian Foreign Minister Sergei Lavrov in Paris on Sunday for talks that reached no breakthrough on the crisis but ended with an agreement for the sides to resume negotiations again soon.

During that meeting, Lavrov said he pressed Russia's call for a federal Ukraine of regions free to choose their own economic model, language and religion.

Kerry said he agreed to work with the Ukraine government on those issues, but called for the removal of "illegal and illegitimate" Russian troops in Crimea, which he said were responsible for creating a climate of intimidation in mainland Ukraine.

Crimea economic zone

In Crimea, Russian Prime Minister Dmitry Medvedev announced on Monday that Moscow would declare the peninsula as a special economic zone with tax breaks to attract investors, according to Reuters news agency.

He made the announcement during his visit to the former Ukrainian region, flaunting his country's grip on the Black Sea peninsula following its annexation.

Crimean officials have said that the local economy is facing a shortfall and needs economic stimulus from Russia.

Medvedev promised to raise the level of salaries for municipal employees and pensions to average Russian levels and to modernise the region's hospitals, which he said were outdated.

"As a result of joining Russia, not one resident of Crimea, not one resident of Sevastopol should lose anything. They can only gain," Medvedev promised during the special cabinet meeting.

Local officials, including Crimean prime minister Sergei Aksyonov, were also present at the meeting that was aired live on Russian state television.