Mr Yanukovych (R) is more pro-Russian than his predecessors
Russian President Dmitry Medvedev is in Ukraine for a visit Moscow hopes will further boost ties with Kiev.
Relations have improved since pro-Moscow President Viktor Yanukovych was elected in February.
But Mr Yanukovych has already dismissed a proposal for Russia's state gas monopoly Gazprom to take control of Ukraine's gas pipeline network.
Other deals, on borders, banking, a GPS-type navigation system and nuclear co-operation are due to be signed.
Last month, Ukraine did approve one controversial deal with Moscow, extending the lease for Russia's Black Sea fleet at its base on the Crimean peninsula in exchange for cheaper Russian gas imports.
The deal has proved unpopular with Ukraine's opposition, which sees it as undermining Ukraine's sovereignty. Mr Yanukovych defended it as reducing the country's budget deficit.
Mr Medvedev has said the navy deal would benefit the security of the whole of Europe.
In pouring rain in Kiev on Monday, the two leaders paid their respects at the Tomb of the Unknown Soldier and attended a ceremony to victims of the Great Famine of 1932-33.
Mr Yanukovych's power base is in mainly Russian-speaking eastern Ukraine, the former Soviet republic's industrial heartland, where ties to Russia remain especially strong.
His election marked a dramatic political comeback as he defeated the leaders of the 2004 Orange Revolution, who pursued closer ties with the West.
The BBC's Richard Galpin in Moscow says that while Mr Yanukovych insists he wants good relations with the European Union, it is becoming increasingly clear that his priority is to move ever closer to Moscow.
Analysts say Mr Yanukovych will seek to balance Russia and the EU in pursuit of Ukrainian interests.
Mr Yanukovych rejected Russian Prime Minister Vladimir Putin's idea of a tie-up between Gazprom and Ukraine's state-owned gas firm Naftogaz.
Instead he has suggested a consortium with Russia and the EU to modernise Ukraine's ageing pipelines.
Ukraine's network carries almost all of Russia's gas exports to Europe.
In the bitterly cold winter of 2008-2009 a pricing dispute between Russia and Ukraine left many countries in Europe short of gas.
The two countries reached agreement on gas supply terms last November.