By Tom Pfeiffer

CAIRO (Reuters) - Egyptians vote Tuesday in the third round of a parliamentary election that has so far handed Islamists the biggest share of seats in an assembly that will be central in the transition from army rule.

Islamist groups came late to the uprising that unseated president Hosni Mubarak in February, but were well placed to seize the moment when Egyptians were handed the first chance in six decades to choose their representatives freely.

The run-up to the third round has been overshadowed by the deaths of 17 people last month in clashes between the army and protesters demanding the military step aside immediately. But the ruling generals have insisted the election process will not be derailed by violence.

Monitors mostly praised the first two rounds as free of the ballot stuffing, thuggery and vote rigging that once guaranteed landslide wins for Mubarak's party.

But police raids on pro-democracy and rights groups last week have disrupted the work of leading Western-backed election monitors and drew accusations that the army was deliberately trying to weaken oversight of the vote and silence critics.

The government said the raids were part of a probe into illegal foreign funding of political parties and not aimed at weakening rights groups, which have been among the fiercest critics of the army's turbulent rule.

Nevertheless, Washington called on the Egyptian government to halt "harassment" of the groups involved.

The U.S.-funded International Republican Institute said it had been invited by Egypt government to monitor the election and did not give funding to political parties or civic groups.

It urged the government to let staff return to their offices and obtain the official registration they had long requested.

"There is no reason not to allow IRI to assess the elections," the IRI said in a statement Monday.

FIERCE RIVALRY

Citizens thronged the polls in unprecedented numbers in the first two rounds and parties ranging from hardline Islamists to liberals and secularists are competing hard for every vote.

Liberals accuse groups like the Muslim Brotherhood and the hardline Islamist Al-Nour party, which surprised with a strong showing in earlier rounds, of flouting a ban on religious slogans in politics and telling voters their rivals are ungodly.

"We have been trying to tell people in our campaign before the third stage that we respect religions," said Mohamed Abu Hamed, Secretary General of the liberal Free Egyptians party.

Islamists in turn accuse one of the party's top figures, Coptic Christian business tycoon Naguib Sawiris, of using his media empire to mount a disinformation campaign against them.

The Brotherhood's Freedom and Justice Party (FJP) "demands from media outlets, especially those owned by businessmen who ... still have interests with the previous regime, to remain objective and stop distorting this experience, which people have been waiting for a long time," the FJP said in a statement.

Although Islamists command a majority of seats contested so far, fierce rivalry among the various Islamist groups offers scope for liberals to wield influence in the parliament, which will play a role in defining a new constitution for Egypt.

But the strong showing by religious parties has sown unease among Western powers that only disowned Mubarak once his three-decade rule was crumbling.

Mubarak painted his government as a modernizing bulwark against Islamist extremists who threatened Egypt's future prosperity and its peace treaty with neighbor Israel.

The Brotherhood, which built a broad grass-roots support base through decades of charity work among millions of poor Egyptians, insists it will do nothing to weaken Egypt's economy further or sow social chaos.

That message of stability has found resonance among ordinary Egyptians tired of almost a year of political turmoil and fearful for their livelihoods as the economy wallows in crisis.

The concluding vote to the lower house of parliament takes in regions of the rural south, which has the largest proportions of Christian voters, the industrial Nile Delta region north of the capital Cairo, and the restive Sinai desert region to the east.

Fourteen million eligible voters in nine regions will choose who occupies 150 of the seats in parliament.

The army, under pressure to hasten the handover to civilian rule, issued a decree Sunday to shorten the forthcoming upper house election to two rounds from three.

(Additional reporting by Tamim Elyan; Writing by Tom Pfeiffer; Editing by Kevin Liffey)