An alliance led by Bangladesh's former prime minister Sheikh Hasina won a massive parliamentary majority in the country's first polls in seven years, unofficial results showed, but a rival party complained of irregularities.
Analysts said it was unclear if the losers would accept the results or take their supporters onto the streets to protest. Political confrontations, strikes and street violence have often hampered the effectiveness of Bangladeshi governments.
"It's critical that both sides accept the result of what appears to be a free and fair election. If not, Bangladesh risks sliding back into the anarchy, violence and corruption that have characterised its past," U.S.-based Asian Society Fellow Sheridan Prasso told Reuters.
Unofficial results from election centres around the country showed Hasina's "Grand Alliance" led by her Awami League had so far won 240 seats in the 300-seat parliament.
Just 31 had gone to a group led by Begum Khaleda Zia, another former prime minister and Hasina's rival for power.
The Monday parliamentary vote returned Bangladesh, a country of more than 140 million people, to democracy after two years of emergency rule imposed by an army-backed interim government.
The winner will have to tackle the endemic corruption as well as the chronic political and social unrest which prompted the military to intervene.
Official results are not expected until Tuesday evening, and Hasina's Awami League urged supporters to wait for those.
"Our leader Sheikh Hasina has appealed to her party and supporters not to stage victory marches or engage in any kind of celebration until the final results are announced by the election commission," her spokesman Abul Kalam Azad told reporters.
A leader of Khaleda's Bangladesh Nationalist Party said its supporters were kept from voting in various parts of the country, and it planned to file a complaint.
"We have reports that BNP supporters were barred from coming to polls and also were driven away from polling stations in many places," BNP official Rizvi Ahmed told a news conference.
The poll was generally peaceful, with both independent monitors and many voters saying they saw few glitches. Previous elections were marred by widespread accusations of vote-rigging.
"The election ended in a very peaceful environment and I never saw such a congenial atmosphere. The turnout was tremendous," Taleya Rehman, executive director of monitoring group Democracy Watch, told Reuters.
The United States also praised the vote.
"All Bangladeshis can take great pride in the success of these elections. The high voter turnout underscores the people's desire to see democracy restored," Gordon Duguid, a State Department spokesman, said in a statement.
The statement urged losing candidates to continue to participate in the political process.
The military-backed interim government took control of Bangladesh in January 2007 amid widespread political violence, and cancelled elections due that month.
Populist rivals Hasina and Khaleda alternated in power for 15 years up to 2006. Critics say they failed to resolve Bangladesh's problems partly because of protests, strikes and street violence linked to their parties when out of office. The turbulence kept investors away and distracted government from other challenges.
Considering that background, analysts said it may be less important who won than that the losers accept the results.
Bangladesh's neighbours worry that an increasingly violent Islamist militant minority could provide support and shelter for radicals in their own countries.
Most Bangladesh Muslims are moderates, however. Analysts said Khaleda suffered from the presence in her alliance of Islamist party Jamaat-e-Islami. Its chief and other leaders lost their seats as its parliamentary members dropped from 17 to 2.
Hasina had pledged to crack down on violent extremists, and to contain prices and promote growth in a country where 45 percent of the population lives below the poverty line.
Business leader Abdul Awal Mintoo said in a panel discussion that despite its apparent huge majority, "the Awami League should form a government of consensus with the opposition".
(Additional reporting by Anis Ahmed)
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