The raids, which started on September 30, have killed 1,015 civilians, including more than 200 children, the Britain-based Syrian Observatory for Human Rights said.
The group, which relies on a network of sources on the ground for its reports, said the strikes had also killed 893 Islamic State group jihadists and 1,141 other opposition militants, including members of Al-Qaeda affiliate Al-Nusra Front.
The total toll of 3,049 represents an increase of nearly 700 deaths in just three weeks.
Russia is a staunch ally of the Syrian government and has coordinated its strikes with Damascus, saying it is targeting IS and other "terrorist" groups.
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But activists and rebels accuse Moscow of focusing more on moderate and Islamist opposition fighters than IS.
Russia has previously denounced accusations that its raids have killed civilians as "absurd" and said claims by rights groups of such deaths were made up of "cliches and fakes".
The Observatory says it differentiates between strikes by Russia, US-led coalition warplanes and the Syrian regime based on the type of aircraft and the munitions used.
A coalition led by Washington has also been carrying out strikes against IS in Syria since September 2014, but it does not coordinate its raids with Damascus.
Those strikes have killed 4,256 people since they began, among them 322 civilians, including over 90 children, according to the Observatory.
The monitor said the strikes had also killed 3,787 IS fighters and nearly 150 militants from other extremist groups including Al-Nusra.