Mr Putin wants talks on membership of the World Trade Organisation
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Chechnya and the Yukos controversy are likely to be key talking points as Vladimir Putin meets European leaders.
The European Commission says it will press the Russian president to moderate the actions of security forces in Chechnya.
It also wants Russia to apply the rule of law fairly in the case of jailed Yukos oil tycoon Mikhail Khodorkovsky.
The summit in Rome on Thursday is the last before the EU takes in eight former communist states next year.
Straight talking
Mr Putin, who is on a state visit to Italy, is expected to raise Russia's membership in World Trade Organisation and easy visa terms for Russians travelling to Europe.
The BBC's David Willey, in Rome, says that there is likely to be some plain speaking.
Mr Putin will meet Europe's delegation of Romano Prodi, Chris Patten and Javier Solana.
The Russian leader is expected to confront them about European attitudes towards the war in Chechnya, which he says it is part of the wider war against terrorism
Mr Putin has hit back at criticism from human rights organisations saying that everyone condemns the bombs in Afghanistan and in Iraq, but not those in Chechnya.
Enlargement support
Our correspondent says the Russian leader will also be seeking some recognition for the help that Moscow has given in supporting the forthcoming enlargement of the EU into eastern Europe.
He says he must be grateful for Italian Prime Minister Silvio Berlusconi's support and soothing words about the controversy in Moscow over the arrest of the Yukos boss.
Mr Berlusconi said publicly he was confident that Russian justice would not be used for political ends.
In a reference to his own battles with Italian justice, the Italian prime minister added that he had always fought against an improper use of his own country's judicial system.