European countries have called for "strong measures" to halt repression in Syria, as its government steps up a campaign against peaceful protests.
In a joint statement, France and Italy urged the EU and UN to put pressure on Syria to end its crackdown.
The UK said it was discussing measures with "an impact on the regime". The US is also considering sanctions.
More gunfire was heard in the city of Deraa on Tuesday, a day after troops and tanks were deployed.
Deraa has been at the centre of protests against President Bashar al-Assad.
But there have been numerous reports of a crackdown and arrests around Syria in recent days, despite the lifting of an emergency law last week.
Syria's security forces have shot dead more than 400 civilians in their campaign to crush the month-long pro-democracy protests, according to Sawasiah, a Syrian human rights organisation.
It has called on the UN Security Council to convene and start proceedings against Syrian officials in the International Criminal Court.
According to a UN Security Council diplomat, the UK and other European states are circulating a draft statement condemning the violence in Syria.
'Reform not repression'
Speaking at a joint news conference with French President Nicolas Sarkozy, Italian Prime Minister Silvio Berlusconi said France and Italy were calling for an end to violence.
"We issue a strong call on the authorities in Damascus to end the violent repression," he said.
But Mr Sarkozy said France would not intervene in Syria without a Security Council resolution.
The UK reiterated the call to halt violence.
"This violent repression must stop. President Assad should order his authorities to show restraint and to respond to the legitimate demands of his people with immediate and genuine reform, not with brutal repression," Foreign Secretary William Hague told the House of Commons.
He said the UK was in discussions with its EU allies and others the possibility of measures, including sanctions, "that will have an impact on the regime" if the crackdown on protesters continued.
The UK has advised British nationals not to travel to Syria and that those in the country should leave.
Meanwhile the US state department warned American citizens to stay away from Syria, and for those who were there to leave while there were still commercial flights.
It added that some non-essential embassy staff and all embassy dependants would be leaving.
International concern
The BBC's Owen Bennett-Jones, in neighbouring Lebanon, says the Syrian government disputes the Western view that the demonstrations have been non-violent.
In a statement carried by the official news agency, it said it had sent troops to several cities on the request of citizens who were worried about "armed extremists".
Arrests were made and those people would be processed through the civil courts, the government statement added, following the lifting of emergency laws last week.
The agency said 15 soldiers and security personnel were killed in fighting on Monday against what it called armed criminal gangs.
Nadim Houry, Beirut director of Human Rights Watch, said that with electricity and phone lines cut from Deraa and other areas, it was becoming much harder to get information out of Syria.
"A new phase started on Friday morning - when security forces killed protesters in 14 towns and cities - and it continued on Saturday and Sunday," Mr Houry told the BBC.
"The government has clearly decided to go for a military-centred response to the protests in an attempt to crush them and reinstate the wall of fear that protesters had started breaking down in some parts of Syria."
Our correspondent says communication with Syria is virtually impossible, though there are reports of continuing clashes as the government tries to re-establish control of Deraa.
Gunfire can be heard on video footage which has been put on the internet and is said to have been filmed on Tuesday. Witnesses have also reported sporadic gunfire in the city.
On Monday witnesses said the army had advanced into Deraa, using several tanks to support thousands of troops. Security forces also reportedly opened fire in a suburb of Damascus.
"The bullets continue against the people, but we are resisting," local activist Abazid Abdullah told AFP news agency.
One Damascus resident said it was currently calm in the capital, but warned that the crackdown on protests would be counter-productive.
"If the Syrian regime thinks that by killing the people, they will stop the people going out to the streets, they are making a big mistake," the resident told the BBC.
