Since Pinheiro's panel of investigators issued its last report in February, heavy fighting has spread to new regions, he told the UN Human Rights Council.
The panel found that the government and its allied militias were responsible for killing civilians, illegal detention and various forms of torture, while opposition forces have been torturing or executing government soldiers and those suspected of supporting them.
The investigators said that growing numbers of Syrians are being targeted in the country's conflict on account of their religion.
Amid mounting tensions in the anti-government uprising now in its 16th month, Assad admitted that Syria is in a "real situation of war".
"When one is in a state of war, all our policies and capabilities must be used to secure victory," he told the new cabinet, the official SANA news agency reported.
The United States said a "desperate" Assad was slowly losing his grip on power, citing defections and fighting raging increasingly close to Damascus, and offered new support to NATO ally Turkey after Syrian forces shot down one of its fighter planes last week.
Washington also pushed back on Russia's insistence that Iran should take part in a planned international conference on Syria in Geneva on Saturday.
The shooting of the Phantom F-4 fighter jet has split Moscow and the West, with NATO condemning Syria and voicing its solidarity with member state Turkey while Russia said the incident should not be seen as intentional.
Erdogan raised the heat on the Assad government by accusing it of shooting down the jet while it was in international airspace, without warning.
Erdogan, once a close ally of Assad, has become one of the Syrian leader's biggest critics and his reaction to the downing of the jet is his fiercest outburst to date.
The Turkish PM admitted that the fighter plane had violated Syrian airspace, but said it was only for a short time and "by mistake," insisting that it was not in Syrian airspace when it was shot down.
Damascus has defended the downing of the jet, saying it was a response to "a gross violation" of its sovereignty.
Darul Ihsan Media Desk