The March dead included 298 children, 291 women, 1,486 rebel fighters and army defectors and 1,464 regime soldiers, said the opposition Syrian Observatory for Human Rights, which has a network of sources across Syria. The 588 other dead were unidentified but documented by individual photos and video, the observatory said.
The Syrian regime of President Bashar Assad provides no death tolls for the civil war.
The conflict has often seen daily death tolls top 150 as regime shelling and aerial bombardments increase amid escalating clashes between loyalist forces and rebel fighters.
The March toll surpassed August 2012 as the deadliest month, when airstrikes, clashes and shelling killed more than 5,400 people, he said.
More people were killed in March than in the first nine months of the uprising, which began March 15, 2011, with anti-government demonstrations that grew nationwide the following month and later turned into a civil war.
The observatory logged 3,893 deaths in February.
The March toll "does not include the thousands of forcibly disappeared persons in the regime's detention centers, nor the hundreds of kidnapped members of the regular forces and others taken captive by the rebels," the observatory said in a statement posted on Facebook.
The toll would possibly be twice as high if all the dead were able to be counted.
The observatory said the cumulative death toll in the past two years was 62,554, half of them civilians. Of that number, some 4,400 were children and more than 2,700 were women.
The United Nations estimated in February more than 70,000 people had been killed since the conflict began. It did not update its figure for March.
The death toll could not be independently confirmed because the Assad regime severely restricts access to journalists and outside observers.