UPDATE 2-At Least 37 Syrian Protesters Killed, Hospital Says

* Soldiers with AK-47s in streets

* Death toll from Wednesday's attack up to 37

* France, Britain call for dialogue

* Adviser to Assad says "important decisions" coming (Adds remarks by presidential adviser, commentator)

By Suleiman al-Khalidi

DERAA, Syria, March 24 (Reuters) - At least 37 people were killed in the Syrian city of Deraa, a hospital official said on Thursday, in an escalation in protests which have prompted the government to promise to listen to protesters' demands.

Buthaina Shaaban, an adviser to President Bashar al-Assad, told reporters the demands of the people of Deraa were "justified ... and under study ... The coming period will witness important decisions on all levels".

Security forces opened fire on hundreds of youths at the northern entrance to Deraa on Wednesday, witnesses said, after nearly a week of protests in which seven civilians had already been killed since Friday.

The main hospital in Deraa, in southern Syria near the Jordanian border, had received the bodies of at least 37 protesters killed on Wednesday, a hospital official said.

Around 20,000 people marched on Thursday in the funerals for nine of those killed, chanting freedom slogans and denying official accounts that infiltrators and "armed gangs" were behind the killings and violence in Deraa.

"Traitors do not kill their own people ... God, Syria, Freedom. The blood of martyrs is not spilt in waste!" they chanted in Deraa's southern cemetery.

As Syrian soldiers armed with AK-47s roamed the streets of the southern city, residents emptied shops of staples and basic goods and said they feared Assad's government was intent on crushing the revolt by force.

Assad, a close ally of Iran, key player in neighbouring Lebanon and supporter of militant groups opposed to Israel, had earlier dismissed demands for reform in Syria, a country of 20 million people run by the Baath Party since a 1963 coup.

A government statement had blamed "armed gangs" for the violence in Deraa.

Syrian political analyst Thabet Salem said of the government promise of "important decisions" that there might be a move to allow free elections to elect the "Assembly of the People".

The assembly is a rubberstamp parliament that has been under Baath Party control for decades.

"The remarks are vague but positive. Only radical change will set Syria on the right course," he said.

MEMORIES OF HAMA

Some people recalled the 1982 massacre in Hama, when Assad's father, Hafez al-Assad, sent troops to the conservative religious city to crush the armed wing of the Muslim Brotherhood. Human rights groups say at least 20,000 died.

"If the rest of Syria does not erupt on Friday, we will be facing annihilation," said one resident in Deraa, referring to Friday prayers, the only time citizens are allowed to gather en masse without government permission.

The environment today, however, is very different from that of 1982, when Syria was supported by the Soviet Union and its minority Alawite rulers were firming up their control of the country against religious and secular opponents without serious criticism from the international community.

Assad, who is facing mounting criticism by the West for the bloodshed in Deraa, "is not against any Syrian citizen", Syrian Vice President Farouk al-Shara was quoted as saying this week.

The protesters in Deraa, a mainly Sunni city, have shouted slogans against the government's alliance with Shi'ite Iran, breaking a taboo on criticising Syrian foreign policy.

Assad, who promised reforms when he became president in 2000, has ignored mounting demands to lift emergency law, allow freedom of speech and assembly, free political prisoners, make the judiciary independent, curb the control of the pervasive security apparatus and end the Baath Party's monopoly on power.

Syria's ruling elite from the minority Alawite sect have presented themselves as a source of stability in a mainly Sunni country made up of many sects and ethnicities including Shi'ites and Christians. The Baath Party has a secular ideology.

The slogans of the protesters in Deraa, where society is predominantly tribal and conservative, have however also emphasised the unity of Syria.

The city is dominated by big families and earns significant income from remittances from Syrians working overseas. Both the Baath Party and the army have recruited heavily from Deraa.

SOLDIERS PATROL STREETS

The army has so far taken a secondary role -- mostly manning checkpoints -- in confronting demonstrations. Secret police and special police units wearing all black have been more visible in Deraa since the protests erupted last Friday.

Witnesses said hundreds of soldiers patrolled Deraa's main streets as heavy rain fell, with scores manning intersections to prevent public gatherings. Travellers on a main highway near Deraa said they saw convoys of trucks carrying up to 2,000 soldiers heading to Deraa on Wednesday night.

In a separate attack in the early hours of Wednesday, security forces fired at protesters in the vicinity of the Omari mosque in Deraa's old quarter, residents said.

Two people killed in that attack, a man and a woman called Ibtissam Masalmeh, were buried in Deraa on Wednesday. Thousands marched in the funeral chanting calls for freedom, and -- for the first time since protests broke out on Friday -- slogans against Iran and Lebanon's armed Shi'ite movement Hezbollah.

"Honourable Syrians don't rely on Iran or Hezbollah," they chanted.

YouTube footage showed what was purported to be the street in front of the mosque before the attack, with sound of gunfire audible and a person inside the mosque grounds yelling: "Brother don't shoot. This country is big enough for me and you".

The United Nations and the United States condemned the violence. France, which occupied Syria from 1925 to 1946, urged the ruling elite to open up to dialogue and democratic change.

Britain called on Syria to respect people's right to peaceful protest and to take action on their grievances. Germany said the violence must end immediately.

The Baath Party has banned opposition and enforced emergency laws since 1963. But the wave of Arab unrest which has toppled leaders in Tunisia and Egypt presents Assad with the biggest challenge to his rule since he succeeded his father Hafez al-Assad, who ruled Syria for 30 years until his death in 2000. (Additional reporting by John Irish in Paris; writing by Khaled Yacoub Oweis in Damascus, editing by Myra MacDonald)