Olmert and his small entourage returned to Israel on Friday morning following a one-day visit to Moscow.
"There is someone to talk to in Moscow, and there are things to talk about. The last word on the Iranian nuclear issue has yet to be said," one of the entourage members noted.
The prime minister met with the Russian president for three hours on Thursday, a day after the latter's return from a meeting with Iranian President Mahmoud Ahmadinejad in Tehran.
Putin invited Olmert to move from the discussion room to his private office, where they met from 5 pm till 8 pm.
"The Russians were very good hosts, and the president warmly welcomed the prime minister," an entourage member said. "The prime minister believes that a great part of the diplomatic work is being done through interpersonal meetings between heads of state.
"This is the network he has created worldwide, and this serves the State of Israel and people of Israel. He can arrive almost anywhere, and in the Kremlin, where he has an excellent relationship with Preisdent Putin, he was welcomed in a wonderful manner."
Positive atmosphere (Photo: Moshe Milner, GPO)
One of the issues the two leaders discussed, according to Olmert's aides, was the Iranian nuclear program.
Olmert briefed Putin on the information Israel possesses about Iran's intentions, including its uranium enrichment activities ahead of the creation of a nuclear bomb.
Aides to Olmert said that he was under the impression that the public Russian rhetoric was different than the reality as Putin sees it.
"What is clear is that the Russians have their own agenda. They view themselves as a super-power, and do not wish to be the passenger sitting beside the American driver. They want to lead processes.
"At the end of the day, however, the Putin administration is not interested in seeing Iran turn into a nuclear super-power, and that is the important thing," said an entourage member.
"The evidence is that nuclear fuel is not being supplied to Bushehr yet, and the question is why. I assume the answer is clear," he continued. "In international diplomacy not everything is seen on the surface. There is a lot of activity down underneath.
"Although the Russians made some commitments to the Iranians, such as the fuel to Bushehr, things are not happening, at least in the meantime. The Russians made it clear to the prime minister that Russia does not want to make things worse for Israel."
Moscow sitting on the fence
Members of the prime minister's entourage rejected claims that Russia had made a decision to abstain from voting on toughening the sanctions imposed on Iran by the UN Security Council.
"They are sitting on the fence. As far as we know, they have yet to make a deicison on the matter and wish to wait and see how this would suit their policy."
Olmert told Putin that he was skeptical over Iran's claims that its nuclear program is for peaceful uses only. The two leaders also discussed Russia's arms deals with Syria, which are threatening Israel's security.
The prime minister made it clear to the Russian president that these deals could harm the military balance in the Middle East. According to the entourage members, Putin promised once again not to harm Israel's security interests.