* Four killed in Tripoli fighting
* Order restored in Beirut
* Political crisis seethes on
By Oliver Holmes
TRIPOLI, Lebanon, Oct 23 (Reuters) - Four people were killed and 15 wounded in overnight gun battles in the Lebanese city of Tripoli in a second night of fighting between Sunni and Alawite gunmen loyal to different sides in the war in neighbouring Syria, a military source said on Tuesday.
In the capital Beirut, tension eased after troops fanned out across the city to clear the streets of gunmen who had clashed on Sunday night.
The violence flared after Friday's assassination in central Beirut of senior Lebanese security official Wissam al-Hassan, who was opposed to the Syrian leadership.
The bombing and the ensuing clashes brought the civil war in Syria into the heart of Lebanon and triggered a political crisis, with the opposition demanding the resignation of the mostly pro-Damascus cabinet of Prime Minister Najib Mikati.
The fighting in Tripoli - Mikati's hometown - took place between the neighbouring areas of Bab al-Tabbaneh, a Sunni Muslim stronghold, and Jebel Mohsen, an Alawite district.
Three Sunnis and one Alawite were killed and 15 people were wounded, a military medical source told Reuters. Residents said combatants traded machinegun-fire and rocket-propelled grenades.
On Tuesday morning, Tripoli's centre was busy and traffic moved freely but the city remained volatile. Soldiers in helmets and flak jackets kept watch and tanks and armoured vehicles mounted with heavy machine guns were parked in the streets.
Shops close to the combat zone were shuttered and the area blocked off with what people called "Bullet Checkpoints" - streets where they feared to go for fear of snipers.
The fruit market on the front line was closed and teenagers in t-shirts with guns hid behind buildings to peek out up the hill into Jebel Mohsen.
Tripoli's Sunni Muslims support the Syrian rebels fighting to overthrow President Bashar al-Assad, who are mostly from Syria's Sunni majority.
Assad is a member of the Alawite sect, an offshoot of Shi'ite Islam. He can count on the support of Hezbollah, a powerful Shi'ite Islamist armed group that is part of the Mikati government, as well as other Shi'ites and Alawites in Lebanon's complex sectarian and political mix.
BOUTS OF FIGHTING
The overnight violence in Tripoli - which has suffered previous bouts of fighting since the Syrian conflict started 19 months ago - brought the toll there to at least 10 dead and 65 wounded since Friday.
Lebanon is still haunted by its 1975-1990 civil war, which made Beirut a byword for carnage and wrecked large parts of the city. Many Lebanese fear the Syrian war will propel their country back to those days, destroying their efforts to rebuild it as a centre of trade, finance and tourism with a measure of democracy.
Opposition politicians have accused Syria of being behind Friday's killing of Brigadier General Hassan, who had worked to counter Syrian influence in Lebanon.
A Sunni Muslim, he helped to uncover a bomb plot that led to the arrest and indictment in August of a pro-Assad former Lebanese minister.
He also led an investigation that implicated Syria and Hezbollah in the 2005 assassination of Rafik al-Hariri, a former prime minister of Lebanon.
Mikati, who is also a Sunni Muslim, had personal ties to the Assad family before he became prime minister in January last year. His cabinet includes Hezbollah as well as Christian and other Shi'ite politicians close to Damascus.
He offered to resign at the weekend to make way for a government of national unity but President Michel Suleiman persuaded him to stay in office to allow time for talks on a way out of the political crisis.
If he were to stand down before an alternative was worked out, it would mean the collapse of the political compromise that has kept the peace in Lebanon.
Free Patriotic Movement parliamentarian Michel Aoun, a Christian politician and an ally of Hezbollah, said Lebanon could not live with such a power vacuum, and noted that forming a new government could take six months or more.
"What happened (Hassan's assassination) constitutes a security setback but if there was a vacuum, maybe the country would be in chaos," he told the Beirut Daily Star newspaper.
Although the two duelling Tripoli neighbourhoods have old grievances, there is growing resentment among some residents against Mikati and his connection with the Iranian-backed Hezbollah, led by Sayyed Hassan Nasrallah.
A protest camp of about 15 tents has been set up outside the prime minister's house.
One protester, Azam Karali, a 47-year-old Sunni jewellery shop owner, said he would stay there until Mikati resigns.
"It was Tripoli that brought him to power but he has now gone to March 8," he said, referring to a group of political parties including Hezbollah who are close to Syria.
Karali is a member of Tayyar al-Mustaqbel, a group aligned with the opposition March 14 movement, an alliance of political parties many of whom support the uprising in Syria.
"We want our politics to be Lebanese. We don't want Syrian interference, or even American, Iranian, Saudi, whatever," he said.
Posters of the assassinated intelligence chief were plastered on walls all over the city.
"Assad, Nasrallah and Iran made that bomb and we have now lost our protector," said Abu Marwan, a car seller who had been at the protest camp since Saturday.
But a man called Bassam, an architect, said he was an avid Mikati supporter and he believed 70 percent of the city supported him.
"This is Mikati's city. He helps us," he said, speaking in a coffee shop. "Tell me, where is the evidence that this bomb was Syrian made?"