"We know how much you are worried by the situation about Iran's nuclear program," Putin told Olmert at the start of their talks in the Kremlin. "I am ready to share with you the results of my visit to Tehran."
Olmert, paying a snap visit to Russia which will last just a few hours, replied: "I will be glad to hear about the results of your visit to Tehran and to talk about all the concerns we have regarding this situation, as well as about other issues."
Putin visited Iran on Tuesday, the first Kremlin leader to go to Iran since Josef Stalin in 1943, and told Washington that Moscow would not accept military action against Tehran. He also invited Iranian President Mahmoud Ahmadinejad to visit Moscow.
Peace process high on Olmert's agenda
Putin's visit to Tehran was watched closely because of Moscow's possible leverage in the Islamic Republic's nuclear row with the West.
Russia is building Iran's first atomic power plant in Bushehr, but Western powers fear that Tehran's pursuit of nuclear-generated electricity is a precursor to building an atom bomb. Iran says its program is for peaceful purposes.
Olmert last visited Moscow a year ago and voiced Israel's concerns about Iran's nuclear ambitions.
The Israeli-Palestinian peace process is also high on Olmert's agenda in Russia, Itar-Tass news agency quoted an unnamed Kremlin source as saying.
Russia is part of the "Quartet" of international mediators on the Middle East. Other members are the United States, the United Nations and the European Union.
"Russia views this meeting as a step in a series of events before convening a full-scale international conference on all-embracing peaceful settlement in the Middle East," the Kremlin source told Itar-Tass.
Olmert's trip came on the final day of a four-day visit to Israel and the occupied West Bank by US Secretary of State Condoleezza Rice, who is preparing the ground for a US-sponsored Middle East conference expected next month.