The New York-based Human Rights Watch said it had documented 85 aerial attacks by the government against opposition areas in northern Aleppo province since 22 February alone.
It urged the United Nations to block the flow of arms to the government and any group committing abuses against civilians in the war-torn country where an estimated 150 000 people have been killed in the past three years.
"The Security Council should impose an arms embargo on Syria's government, as well as on any groups implicated in widespread or systematic human rights abuses," HRW said.
Its statement comes more than two months after a 22 February Security Council resolution demanding an end to attacks on civilian areas.
HRW said that since then it "has documented at least 85 strike sites in (opposition-held) neighbourhoods of Aleppo city... including two government barrel bomb attacks on clearly marked official hospitals".
The strikes, most reportedly involving "unguided, high-explosive barrel bombs", have hit civilians and civilian objects "indiscriminately".
The group said attacks that cannot distinguish between fighters and civilians are "unlawful".
Such attacks "continue despite a United Nations Security Council Resolution unanimously passed on 22 February 2014, demanding that all parties in Syria cease the indiscriminate use of barrel bombs and other weapons in populated areas," HRW said.
Syrian government forces launched an aerial offensive targeting opposition areas last December.
Hundreds of people, mainly civilians, have been killed in these attacks. Thousands of families have also fled into the countryside and for neighbouring Turkey to the north.
HRW's statement came a day after President Bashar Assad registered to stand for re-election next month.
"President Assad is talking about elections, but for Aleppo's residents, the only campaign they are witnessing is a military one of barrel bombs and indiscriminate shelling," HRW deputy Middle East and North Africa director Nadim Houry said.
The rights group said the supply of arms to rebel groups that have committed systematic abuses must also stop.
It said that "at least some of the improvised weapons used (by rebels fighting an offensive on government areas in Aleppo) are prone to indiscriminate effects when used to attack populated residential areas".