Olmert's one-day visit was announced only after Putin had returned from Iran, where he vowed Tuesday to support Iran's pursuit of nuclear energy and warned "outside forces" - hinting at the United States - against using force against Iran.
Olmert "will be very clear on the Israeli position that in no way can Iran achieve nuclear capability, that Iranian nuclear capability threatens the world, including Russia," Israeli government spokeswoman Miri Eisin said Thursday.
Israel considers Iran to be a threat to its existence, while Russia is a major provider of technology for Tehran's nuclear program, which the West suspects is geared toward the development of nuclear weapons.
U.S. President George W. Bush said Wednesday that he wanted to get a report directly from Putin about his visit to Iran and warned that a nuclear-armed Iran could trigger World War III.
While in Tehran, Putin made an unspecified proposal concerning Iran's nuclear program to the country's supreme leader Ayatollah Ali Khamenei, Iran's state news agency IRNA reported after the meeting. Officials close to hard-liners within Iran's ruling Islamic establishment said they believed the proposal involved a "timeout" on sanctions if Iran suspends uranium enrichment.
On Thursday, however, Iranian President Mahmoud Ahmadinejad said Putin "did not say any word" about the nuclear program during his meeting with the supreme leader, IRNA reported.
Olmert's talks with Putin also were expected to address new arms deals - reportedly, Iranian-funded - under which Moscow would supply Syria with advanced surface-to-air and anti-aircraft missiles that Russia has not previously sold to other countries. Israel says Russian arms sold to Syria and Iran have been used by Hezbollah guerrillas in Lebanon.