The PACE head called on Russia to ratify Protocol 6 to the European Convention on Human Rights, which outlaws capital punishment.
Although Russia imposed a moratorium on the death penalty shortly after it joined the 47-nation Council of Europe in 1996, it did not formally abolish capital punishment within three years, as membership of the organization requires.
Putin said Russia would comply with the Convention, but added that a complete legal ban on the death penalty would depend on the opinion of the Russian people. Latest opinion polls suggest that a total of 65% of Russians support the death penalty.
Another document that came under discussion during van der Linden's visit to Moscow on Thursday was a protocol on the reform of the European Court of Human Rights in Strasbourg, the subject of an increasing number of inefficiency complaints.
The protocol enables the court to reject a suit if the damage claims are judged to be insignificant. It also extends a judge's term in office from six to nine years, which observers expect to improve the court's efficiency.
In December, Russia's lower house of parliament, the State Duma, rejected the protocol, saying some provisions were unacceptable for Moscow, a move that froze the reforms.
Konstantin Kosachyov, head of the international affairs committee in the lower house of Russia's parliament, said "Russia is interested in the court's activity and does not intend to block its work."
Meanwhile, he said, "there are some concerns that the court, as a judicial body, will turn into a political instrument, a tool of pressure."
Russia could agree to the reform if it "makes sure that the court acts only on a legal basis and is not used to achieve political goals," Kosachyov added.
The agenda for Thursday's meeting also included relations between Russia and the Council of Europe, as well as Russia's recent parliamentary polls and its upcoming presidential elections.
Van der Linden once again voiced concerns over Russia's December 2 parliamentary polls, and said he hoped the March 2 presidential elections would be open and democratic.
The PACE head also invited Putin, who is reaching the end of his second and final term as president, to take part in the next PACE session, to be held in Strasburg in April.