Rozhkov said that Russia was however co-operating with other world powers over measures purely targeting the nuclear issue.
"We are working with the US and others ... only to solve those concerns we have regarding Iranian nuclear efforts," he said.
Neave Barker, Al Jazeera's correspondent in Moscow, said: The latest comments from Russia's foreign ministry merely reiterate what Russia has always said.
"That, yes, there is a possibility of imposing, or pressuring, Iran to somehow come into line with the UN but in no way were sanctions in full force ever discussed."
Russia has walked a fine line on Iran for years, backing three previous sets of UN Security Council sanctions on Iran, but using its influence to water down tougher US proposals.
It also has tried to maintain friendly ties with Iran, a regional power close to Russia's vulnerable southern flank, and is helping to building the country's first nuclear power plant.
But Iran's continuing unwillingness to co-operate with the international community over its nuclear programme has led Russia to criticise the stance being held by the Iranian government.
Alireza Ronaghi, Al Jazeera's correspondent in Tehran, said: "I have absolutely no doubt that all Iranian officials will welcome any position, or any comments, if you like, by Russian diplomats or officials regarding their position against crippling sanctions to be imposed on Iran.
"But, let me add, on the Iranian streets there is very little trust, and diminishing trust, towards Russia.
"People think Russia will sell out Iran when needs be and they know Russia is playing with Iran's card in the international arena.
"And that with or without Russia's help, America may still go on and impose its sanctions on Western companies that may deal with Iran, and that could be a very big problem for Iran and the Iranian people."
Sergei Lavrov, Russia's foreign minister, suggested on Wednesday that a delay in delivering air-defence missiles to Tehran is connected with concerns about regional tensions there.
Russia signed a contract in 2007 to sell S-300 missiles to Iran, a move that would substantially boost the country's defence capacities.
When asked about the delivery, Lavrov said that Russia never takes "any actions leading to the destabilisation of this or that region".
"All deliveries of Russian weapons abroad follow from the need to strictly respect this principle," he said.
It marks the first time that Moscow has publicly called into question the wisdom of honouring its contractual obligations to Iran.
Various defence officials had suggested in recent months that they would be fulfilled.
Israel fears the sale would tip the regional power balance in favour of Iran.
Jacky Rowland, Al Jazeera's correspondent in Jerusalem, said: "Of course Mr [Binyamin] Netanyahu [the Israeli prime minister] was in Moscow just a week ago trying to secure Russian support for these proposed sanctions that Hillary Clinton [the US secretary of state] had described as crippling.
"However, people I have been speaking to here say that the government is probably taking comfort in the fact that the man who made these comments, Mr Rozhkov, is not the most senior person by any means.
"And the fact that the Russian government is known to be really divided in terms of the opinions on how best to proceed, whether sanctions work or not."