"As far as the Iranian nuclear problem is concerned, we would like this problem to be solved as soon as possible within the framework of international norms," Rowhani told Putin in televised remarks translated into Russian in Bishkek.
"In the past Russia undertook important steps in this sphere, and right now is the best opportunity for new steps on your part," he said.
The two leaders were meeting for the first time on the sidelines of a summit of the Shanghai Cooperation Organisation held in Kyrgyzstan.
Putin in turn praised Moscow's long-standing regional ally as a close neighbour in Rowhani's first meeting with a major world leader since he won June elections.
"We know how much in international affairs is revolving around the Iranian nuclear problem, but we in Russia know something else, too: that Iran is our neighbour, a good neighbour," Putin said.
"We do not choose our neighbours," he added.
Putin was reportedly going to offer for Russia to build a second nuclear reactor at Iran's Bushehr nuclear power plant, according to a diplomatic source quoted by Kommersant daily on Wednesday.
Putin was also reportedly offering the renewal of a contract to supply Iran with sophisticated S-300 air defence missile systems, after the deal was cancelled under international pressure in 2010.
The diplomatic source told Kommersant that Putin would make the offer in return for Iran's withdrawing a $4 billion (3 billion euros) lawsuit that it has lodged in Geneva over the scrapping of the deal.
Putin's spokesman Dmitry Peskov denied to Russian news agencies that the arms offer was on the table, however.
Moscow has cooperated with Iran on nuclear power generation despite international opposition to a programme that Western powers and Israel believe is being used as a smokescreen for building a nuclear bomb, while Iran insists it is peaceful.
Iran denies seeking or ever having sought nuclear weapons and argues that the six UN Security Council resolutions passed against it since 2006 -- four with sanctions attached -- are illegal.
Russia urged the West to soften sanctions against Iran after the election of Rowhani, a centrist cleric, in June, expressing hopes for a major breakthrough in the nuclear standoff. Rowhani has pledged greater transparency in talks.
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