Syria protests: Assad to lift state of emergency
The state security court, which handled the trials of political prisoners, has been abolished while a new law allowing peaceful protests has been approved.
The repeal of the emergency law was a key demand of protesters.
Earlier, unverified footage from the western city of Homs appeared to show security forces opening fire.
The BBC's Owen Bennett-Jones says the legal changes will be remarkable to most Syrians after decades of one-party rule, but it is unclear how much difference they will really make.
The indications are that they will not be enough to satisfy the protesters, our correspondent adds. Anti-government demonstrations are reported to have begun in the north-western city of Baniyas after the emergency law was passed.
Several hundred people were also reported to be rallying on the streets of Damascas.
The new law must now be signed by President Bashar al-Assad before it comes into effect.
Under the legal changes, permission from the interior ministry will be needed to demonstrate in Syria.
But the country's interior minister has nonetheless urged people to refrain from taking part in any rallies in the interests of safety and stability.
Mohammed Ibrahim al-Shaar told people "to refrain from taking part in all marches, demonstrations or sit-ins under any banner whatsoever", in remarks carried by the official news agency, Sana.
He warned that if demonstrations were held, "the laws in force in Syria will be applied in the interest of the safety of the people and the stability of the country".
See www.bbc.co.uk for full version.