CAIRO (Reuters) - Street clashes flared in Cairo again Wednesday as protesters derided an agreement forged by Egypt's ruling generals and mostly Islamist parties for a swifter transfer to civilian rule.

The death toll in five days of violence climbed to 37 by a Reuters count after a man was killed in the city of Alexandria. Hardcore protesters battled police through the night in Cairo.

The Health Ministry said 32 people had been killed and 2,000 wounded in disturbances across the country of 80 million.

Field Marshal Mohamed Hussein Tantawi, head of the military council that has run Egypt since Hosni Mubarak fell on February 11, promised Tuesday that a civilian president would be elected in June, about six months sooner than the army had planned.

"Leave, leave!" responded crowds in Cairo's Tahrir Square. "The people want to topple the marshal."

The military had originally pledged to return to barracks within six months of Mubarak's removal. Its apparent reluctance to relinquish its power and privilege has fueled frustration among Egyptians who feared their revolution had changed nothing.

Tantawi, who was Mubarak's defense minister for two decades, adjusted the schedule after generals met politicians, including leaders of the once-banned Muslim Brotherhood, which is eager to turn decades of grassroots endeavor into electoral success.

A parliamentary election, billed as Egypt's first free vote in decades, will start Monday as planned, Tantawi confirmed.

Voting for the upper and lower houses will only be completed in March under a complex, staggered process. Parliament will then pick an assembly to draw up a new constitution, an exercise which the Brotherhood and its rivals are keen to influence.

France added its voice to those of U.N. and other rights groups in denouncing the military's handling of the protests.

French Foreign Ministry spokesman Bernard Valero said his country "strongly condemns the excessive use of force against demonstrators" and called for elections to go ahead on time.

"In this critical period, we reiterate our support for a democratic transition in the country that in 2012 should transfer power back to elected civilian authorities," he said.

U.N. human rights chief Navi Pillay called for an independent investigation into the bloodshed, saying the killing of protesters was inflaming the crisis.

"I urge the Egyptian authorities to end the clearly excessive use of force against protesters in Tahrir Square and elsewhere in the country, including the apparent improper use of tear gas, rubber bullets and live ammunition," Pillay said.

Instead of a peaceful environment for elections, she added, "we are seeing another outbreak of violence by the state against its increasingly and legitimately angry citizens."

REFERENDUM ON MILITARY RULE

Tantawi angered many youthful demonstrators in Cairo's Tahrir Square and other cities by suggesting a referendum on whether military rule should end earlier, which they viewed as a ploy to appeal to the many Egyptians who fear further upheaval.

A referendum on temporary changes to the constitution made by the army won 77 percent approval in April, when the generals were still widely popular for helping remove Mubarak.

"We have to wait and be patient with army rule. We shouldn't have a referendum, it's a waste of time," said Mohamed Rasheed, 62, a salesman in a Cairo jewelry shop, who pointed to a discordant thrum of opinions among protesters in Tahrir.

"If we listen to them all, we are going to become like Lebanon," he said, evoking a nation notorious for conflict.

Skirmishes between stone-throwing protesters and riot police firing tear gas, pellets and rubber bullets erupted intermittently around the Interior Ministry near Tahrir.

"As soon as daylight broke they started shooting, because they could see us," said Tareq Zaki, 32, a furniture maker.

Police have denied using live ammunition but most of the 36 dead in five days of violence had bullet wounds, medics say.

The streets were strewn with surgical masks protesters use to ward off tear gas. Ambulances ferried the wounded away.

In Tahrir, where hundreds of protesters camped out overnight in tents or in the open, people collected garbage in bags or burned it in small piles. Others passed around food.

"We will stay here until the field marshal leaves and a transitional council from the people takes over," said Abdullah Galal, 28, a computer sales manager, in the square.

"There are many viruses in the system. It needs to be cleaned out entirely," Galal said. "We need to change the regime like they did in Tunisia and Libya."

Tantawi may calculate that most Egyptians, alarmed by turmoil that has hammered an already troubled economy, would prefer army rule to the uncertainties of a radical upheaval.

The Muslim Brotherhood, which helped organize a big protest Friday but stayed out of subsequent demonstrations, seems willing to compromise with the military in the interest of securing a substantial voice in the new parliament.

Some other Islamist and liberal parties, as well as three out of more than 10 declared presidential candidates, also took part in Tuesday's crisis talks with the military council.

Tantawi has promised a national salvation government to replace Prime Minister Essam Sharaf's cabinet, which resigned this week, but remains in a caretaker role.

Political uncertainty has battered Egypt's finances. Foreign reserves have tumbled to $22 billion in October from $36 billion in December, just before the anti-Mubarak uprising erupted.

Egypt's currency dipped to its lowest level in almost seven years Wednesday and the yield on an Egyptian dollar bond soared to its highest since March, suggesting that investors are unconvinced that stability will return soon.

(Additional reporting by Tom Miles in Geneva and John Irish in Paris; Editing by Jon Boyle)