At least four people were killed and around 50 wounded when Syrian security forces opened fire on a funeral procession in Talbisseh near the central town of Homs on Sunday, witnesses said.
Regime supporters also broke up two rallies in southern Syria, wounding five people after a presidential vow to end emergency rule within a week was dismissed as not enough and was followed by new protests.
In the country's major port, Latakia, around 10,000 people took to the streets late on Sunday after the funeral of a protester killed on Friday, a rights activist told AFP.
Security forces "opened fire on a crowd of thousands of people" in Homs at the funeral of a man killed in the area the previous day, witnesses told AFP by telephone.
"At least four people were killed, but the toll could be much higher. There were also more than 50 wounded," one witness said.
The official news agency SANA reported: "One policeman was killed and 11 others were wounded by fire from an armed criminal group in Talbisseh."
The report added: "Three armed criminals were killed and 15 others injured, as well as five soldiers.
"The criminals opened fire from buildings close to an army post near the bridge where the army had been sent to apprehend these gangs."
Sunday's protests followed a Saturday televised address by President Bashar al-Assad promising to end emergency rule, in force since 1963 when the Baath party took power, within a week.
The current emergency law restricts public gatherings and movement, authorises the interrogation of any individual and the monitoring of private communications and imposes media censorship.
In a televised address to the new cabinet charged with launching reforms, Assad also expressed his sorrow over the deaths of an estimated 200 people in a month of protests demanding greater freedoms.
"We are sad for all the people we have lost and all the people injured, and consider them all martyrs," he said in his address.
"The Syrian people are respectable. They love the regime and reject chaos," Assad said, and called for a national dialogue.
At least five demonstrators were wounded when regime agents dispersed two pro-freedom rallies in the south, bastion of Syria's Druze minority, rights activists said.
Some 400 people had gathered to celebrate Independence Day in Suweida, said Mazen Darwish, director of the Syrian Centre for Media and Freedom of Expression.
Demonstrators carried portraits of the leaders of the revolution that ended French rule and chanted slogans calling for freedom, he told AFP.
But regime backers cut short the rally, he said, beating protesters and trampling on portraits of Syrian revolutionary leaders who fought to end the French mandate.
In the southern town of Daraa, nerve centre of more than a month of anti-regime protests, upwards of 4,000 people, including former political prisoners and religious leaders, staged another rally.
They chanted anti-regime slogans, said a rights activist who requested anonymity.
In the northern coastal town of Banias, which has been shaken by a deadly security crackdown and shootings that residents blame on regime thugs and agents, 2,500 people demonstrated, a rights activist told AFP.
They marched under banners that read: "You are in Banias, not in Israel" in a rebuke to officials blaming the violence on foreign plotters.
Assad, who has ruled Syria since the death of his father Hafez in 2000, told his cabinet to replace draconian emergency laws within seven days.
But rights activists said the gesture fell short of protesters' demands.
Rami Abdel Rahman of the Syrian Observatory for Human Rights said on Sunday that cancelling "military courts" and revoking a law granting security agents immunity were also necessary.
And prominent Syrian human rights lawyer Haytham Maleh told AFP: "It is a step, but it is not enough. It must be accompanied by reform of the judicial system which is corrupted."
Maleh called for the release of political prisoners and said "interference by the security services in the lives of the citizens must stop."
"Demonstrators must be allowed to protest," said Maleh who was released under a presidential pardon in March after more than two years in jail.
Shortly after Assad's address, 2,000 people rallied against the regime in Daraa, the official SANA news agency reported.