* Troops and protesters battle in central Cairo
* Violence clouds election set to empower Islamists (Adds details on late night protest, election results)
By Tamim Elyan
CAIRO, Dec 18 (Reuters) - Protesters and security forces fought in Cairo on Sunday, the third day of clashes that have killed 10 people and exposed rifts over the army's role as it manages Egypt's promised transition from military to civilian rule.
Soldiers and police manned barriers on some streets around Tahrir Square, the hub of the uprising that ousted President Hosni Mubarak and again convulsed by violence as protesters demand the generals who took charge in February quit power.
Police in riot gear made brief forays beyond their barriers and were met by a surge of protesters pelting them with rocks. Police appeared to have taken over the frontline from soldiers.
Troops in riot gear were filmed on Saturday beating protesters with long sticks even after they had fallen to the ground. A Reuters picture showed two soldiers dragging a woman lying on the ground by her shirt, exposing her underwear.
The violence has overshadowed a staggered parliamentary election, the first free vote most Egyptians can remember, that is set to give Islamists the biggest bloc.
Some Egyptians are enraged by the army's behaviour. Others want to focus on voting, not street protests.
The ruling Supreme Council of the Armed Forces will retain power even after the lower house vote is completed in January, but has pledged to hand over to an elected president by July.
"Down with Tantawi," about 1,000 protesters chanted late on Sunday, referring to Field Marshal Mohamed Hussein Tantawi who heads the army council and who was Mubarak's defence minister.
Some youths had earlier hulred rocks and petrol bombs at lines of security forces. Riot police appeared to have moved to the frontline instead of soldiers.
An army source said 164 people had been detained.
Hundreds of protesters were in Tahrir on Sunday, although traffic was flowing through the square coming from streets not blocked and away from the violence. Most of the clashes have been in streets leading off the square.
One group of activists approached those hurling stones to urge them to stop, but they refused, citing the deaths of 10 people as a reason not to "negotiate". Other activists handed over to the army people they said were making petrol bombs.
A hardcore of activists have camped in Tahrir since a protest against army rule on Nov. 18 that was sparked by the army-backed cabinet's proposals to permanently shield the military from civilian oversight in the new constitution.
Bouts of violence since then, including a flare-up last month that killed 42, have deepened frustrations of many other Egyptians, who want an end to protests. They see the military as the only force capable of restoring stability.
"There are people who wait for any problem and seek to amplify it ... The clashes won't stop. There are street children who found shelter in Tahrir," said Ali el-Nubi, a postal worker, adding the army should have managed the transition better.
Reuters television footage showed one soldier in a line of charging troops firing a shot at fleeing protesters on Saturday, though it was not clear whether he was using live rounds.
The army said it does not use live ammunition. It has also said troops had tackled only "thugs", not protesters.
A building near Tahrir with historic archives was gutted on Saturday by a fire. Some people tried to gather up any remaining, partially charred documents to save them.
The Health Ministry said 10 people had been killed in the violence since Friday and 505 were wounded, of which 384 had been taken to hospital. Most of the deaths happened on Friday or early Saturday. No deaths were reported on Sunday.
The latest bloodshed began after the second round of voting last week for parliament's lower house. The staggered election began on Nov. 28 and will end with a run-off vote on Jan. 11.
The Muslim Brotherhood and other Islamist parties repressed in the 30-year Mubarak era have emerged as strong front-runners.
The Brotherhood's Freedom and Justice Party said it had received about 40 percent of votes cast for party lists in the second round of voting last week. The strict Salafi al-Nour Party said its list received about 35 percent.
Despite their commanding position built, it is unclear whether the two rival Islamist groups will form an alliance in parliament, as they have each spoken warily of the other.
The leadership of the Brotherhood is cautious of a wholly Islamist ruling coalition, which Egyptians from other political trends might view as divisive and polarising in a period when they think broader national unity is needed. Nour politicians accuse the Brotherhood of compromising Islamic values. (Additional reporting by Marwa Awad, Alexander Dziadosz and Shaimaa Fayed; Writing by Edmund Blair; Editing by Sophie Hares)