"We unfortunately cannot accept your invitation to send a limited number of observers to Russia for the presidential election taking place on March 2," the letter to Boris Gryzlov said.
The Office for Democratic Institutions and Human Rights (ODIHR), the OSCE elections division, also said it would not be observing the election.
Christian Strohal, head of the ODIHR, said: "We made every effort in good faith to deploy our mission, even under the conditions imposed by the Russian authorities.
"We have a responsibility to all 56 participating states to fulfil our mandate, and the Russian Federation has created limitations that are not conducive to undertaking election observation in accordance with it."
Moscow and the ODIHR, which also stayed away from Russia's legislative election in December because of restrictions, had been tussling for weeks over the latest monitoring mission.
Russia, like all OSCE members, is meant to invite monitors to assess whether elections are free and fair.
Russia initially invited the ODIHR to send 70 monitors on February 28, just three days before the vote, something the office said left no time to observe the election campaign.
|Russia's foreign minister said Moscow would|
accept 'ultimatums' from the OSCE [EPA]
After talks, Russia agreed the deployment this week of a five-member team of technical experts, and the ODIHR had planned to send a "core team" of 15 monitors on Friday.
But the ODIHR had insisted that February 15 was the "absolute minimum" for deploying the remaining 50 monitors.
Sergei Lavrov, Russia's foreign minister, hit back at the OSCE demands on Thursday.
He said: "This is called an ultimatum. Self-respecting countries do not accept ultimatums. The mandate of this bureau ... covers the observing of elections and not observing the state of affairs in one country or another over the course of one or two months."
Strohal, rejecting the comments, said: "An election is more than what happens on election day.
"Therefore, the timeframe set by Russian authorities has already prevented us from observing many important parts of the election process, beginning with the registration of candidates and aspects of the campaign, including the work of the media.
"What is true for every election is also true for this one: transparency strengthens democracy; politics behind closed doors weakens it."
The ODIHR, set up in 1994 after the Cold war, is considered the most authoritative election body in eastern Europe and has previously criticised Russia and other former Soviet republics for a their democratic