Children have been taken hostage, forced to watch torture and even participate in beheadings, it says; others have been killed while fighting.
It says it suspects there are "reasonable grounds" to believe chemical weapons have been deployed.
It urges foreign powers not to increase the availability of arms in Syria.
The issue of arms has been high on the international agenda of late, with the EU lifting an embargo on the sale of arms to Syria while Russia has insisted it is going ahead with the sale of an advanced S-300 surface-to-air missile defence system to Syria.
On Tuesday, Russian President Vladimir Putin said the contract had not yet been fulfilled and Russia did not want to "disturb the balance in the region".
He said he was "disappointed" by the EU move.
Meanwhile, a civilian died when shells exploded near the Russian embassy in Damascus, according to the UK-based activist group, the Syrian Observatory for Human Rights.
Russia is an ally of President Bashar al-Assad and Syrian rebels have targeted the embassy several times since the uprising against his regime began two years ago.
The international powers are struggling to set a date for a peace conference on Syria, where the conflict is believed to have cost at least 80,000 lives.
The UN Commission of Inquiry has so far been barred from Syria and was forced to rely on first-hand accounts from the country.
Its report says it "documents for the first time the systematic imposition of sieges, the use of chemical agents and forcible displacement" in Syria.
"War crimes and crimes against humanity have become a daily reality," it says.
Syria chemical weapons allegations
The report accuses both sides of abuses, but says rebel actions did not "reach the intensity and scale" of abuses committed by government-allied forces.
Syria's UN ambassador Faysal Khabbaz Hamoui has rejected the report, saying the commission is "excessively exaggerating their conclusions and outcomes" while it "totally neglects the substantial events, or even marginalises them".
"The Committee, despite our warnings, insisted on using sectarian language which is rejected by all brackets of the Syrian society."
In the four months covered by this report - between 15 January and 15 May 2013 - investigators documented 17 suspected massacres, out of a total of 30 since the conflict began.
Sieges - with civilians trapped in their homes and reliant on their captors for food, water, medicines and power - are now being used systematically as weapons of war by government forces and affiliated militia and in some instances by anti-government forces, says the report.
Civilians are now becoming the victims of forced displacement by both sides, where they are threatened with attack if they do not leave the area.
The report documents new violations of children's rights on top of being routinely killed, detained and displaced.
In one attack by government forces on Sanamein, Deraa on 10 April, "children were forced to watch the torture or killing of parents".
In another incident in April, this time in Rastan, Homs, checkpoint personnel "threatened to shoot two girls aged nine and seven who started crying during their father's interrogation".
Anti-government forces were also guilty of kidnapping and other violations of children's rights, the report says.
In the most egregious incident near Deir al-Zor, the report cites the participation of a child in the beheading by rebels of two soldiers.
"Video footage emerged showing a child participating in the beheading of two kidnapped men," says the report. "Following investigation, it is believed that the video is authentic and the men were soldiers, killed as depicted."
It says 86 child combatants fighting on behalf of rebel forces have now been killed in the two-year conflict - nearly half of them in 2013 alone.
The report said sexual violence including rape has been used against women, mainly by government forces.
There are "reasonable grounds" to believe that chemical weapons were used in attacks by government forces in Syria in recent months, the UN says.
The report said there were "reasonable grounds to believe that limited quantities of toxic chemicals were used" during attacks on Khan al-Assal, Aleppo, 19 March; al-Otaybeh, Damascus, 19 March; Sheikh Maqsoud neighbourhood, Aleppo, 13 April; and Saraqeb, Idlib province, 29 April.
But it adds that it "has not been possible, on the evidence available, to determine the precise chemical agents used, their delivery systems or the perpetrator".
And it was unable to rule out their use by opposition forces. It calls on Damascus to allow a team of UN chemical weapons experts into the country - a request Damascus has so far denied.
But Commission member and former war crimes prosecutor Carla del Ponte warned reporters not to overemphasise the chemical weapons issue, AFP news agency reports.
"We have so many deaths in Syria now... so please don't make the use of chemical weapons in Syria now the most important issue," she said.
The report concludes that the gravity of offences committed by both sides requires judicial proceedings "at the national and international levels".
It says there can be no military solution, and urges the polarised international community to pursue a negotiated peace.
"There is a human cost to the political impasse that has come to characterise the response of the international community to the war in Syria...
"Increased arm transfers hurt the prospect of a political settlement to the conflict... and have devastating consequences for civilians," it says, in what correspondents say is a pointed message to foreign powers.
Syria's war has reached "new levels of brutality", the UN says, with evidence of fresh suspected massacres, sieges and violations of children's rights.