"The Russians understand the real danger that nuclear weapons in Iran's possession would represent," the official said, speaking on condition of anonymity.
"We have agreed to give new momentum to meetings between officials of the two countries on this matter," he added following a meeting here between Sharon and Putin.
Sharon, who is on a three-day visit to Russia, was given assurances by Putin during his last visit to the country in 2002 that Moscow was taking the necessary steps to prevent the export of nuclear technology to Iran.
Russia is building Iran's first nuclear power reactor at Bushehr, which has been fiercely criticized by Washington and Israel.
Iran, which has been branded by US President George W. Bush part of an "axis of evil" along with Iraq and North Korea, has faced growing international criticism in regard to its nuclear programme.
In September the International Atomic Energy Agency (IAEA) imposed an October 31 deadline on Iran to fully disclose details of its nuclear programme and urged it to sign the additional protocol to the nuclear Non-Proliferation Treaty (NPT) allowing tougher inspections by the UN watchdog.
Iran was also urged to suspend uranium enrichment.
After initially rejecting the deadline, Iran agreed to comply with IAEA demands just 10 days before the deadline expired during an unprecedented joint visit by British, French and German foreign ministers.
Iran has also pledged to sign up to tougher inspections, but has yet to implement its agreement to suspend its work on the nuclear fuel cycle.
And on Sunday, it said that it remained unwilling to totally halt uranium enrichment.
The Israeli official warned: "You cannot trust these Iranian manoeuvres which are just to deceive the world to continue their nuclear programme."
Aharon Zeevi, the chief of Israeli military intelligence said on October 21 that Iran's nuclear programme would reach the "point of no return" in 10 months' time, after which outside powers would not be able to stop it.