The head of the Syrian Observatory for Human Rights said an increase in shelling and clashes around the country led to the high toll, which is incomplete because fighters on both sides tend to underreport their dead.
"Both sides are hiding information," Rami Abdul-Rahman said by phone from Britain, where he is based. "It is very difficult to get correct info on the fighters because they don't want the information to hurt morale."
The increase also likely represents the further spread of the civil war throughout the country.
Clashes continue to rage in the northern city of Aleppo and around the capital Damascus as well as in the central city of Homs.
And in recent weeks, rebels in the southern province of Daraa along the Jordanian border have seized towns and military bases from the government with the help of an increased influx of foreign-funded weapons.
The Observatory, which opposed President Bashar Assad's regime, said the March dead included 298 children, 291 women, 1,486 rebel fighters and army defectors and 1,464 government soldiers. The rest were unidentified civilians and fighters.
The government does not provide death tolls for the civil war.
That toll solidly beat the second most deadly month, when airstrikes, clashes and shelling killed more than 5,400 people in August 2012, Abdul-Rahman said.
He said his total death toll for the conflict through the end of March is 62,554, a number he said he guessed only reflected about half of the actual dead.
He said many deaths go unreported by the government or rebel fighters and that there are tens of thousands detained in regime and rebel prisons whose fates are not known.
The United Nations said in February that 70,000 people had been killed since the start of the conflict. It has not updated its number since.
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