NAIROBI, Kenya—Ethiopians went to the polls Sunday for the country's first national election since the death of longtime ruler Meles Zenawi, a vote the ruling party was expected to win overwhelmingly following what rights groups call years of suppression of political opposition.

The controversy over the poll underscores the struggle Western nations have with Ethiopia—praised for its economic progress and security but criticized roundly for seizing lands from farmers, jailing journalists and silencing opposition parties.

"There's no desire from the outside world to destabilize this regime," said Richard Dowden, the director of Britain's Royal African Society. "It's not giving us any trouble; it's a good destination for investment."

Ethiopia is seen as a good place to do business because corruption is generally low and the country's state-controlled industries are stable. Big private-equity firms like New York-based KKR & Co. and Blackstone Group are investing in the country.

Voting appeared to go forward smoothly on Sunday, though at least one opposition leader charged that some of its members had been beaten up and that some polling stations opened with already-full ballot boxes.

"When they went to the polling station this morning, they saw that the boxes were already filled up with marked papers," said Beyene Petros, the chairman of an opposition coalition called Medrek. Election board spokesman Demissew Benti said he had no reports of any problems with the voting. Asked directly about the allegation of the opposition leader he said: "It is not true."

Results aren't expected for at least two days.

The ruling party—the Ethiopian People's Revolutionary Democratic Front or EPRDF—has been in power since 1991. While the last vote in 2010 was peaceful and went almost entirely to the ruling party, that came after a poll in 2005 in which a strong opposition took a significant number of seats and charged that vote-rigging kept them from gaining even more. Violence broke out and some 200 people were killed.

Rights groups say that the government has gone on a systematic campaign to weaken the opposition since then—making it harder for opposition parties to register, or jailing key actors. Journalists have also been imprisoned for allegedly fomenting violence.

"The government has clamped down on all forms of legitimate dissent," said Muthoni Wanyeki, who oversees East Africa for Amnesty International.

Government officials have said that they have only banned political parties that have broken rules and that they have only jailed people who have posed a security threat to the country.

The question going forward is whether the current stability will continue despite increasing criticism of the government's approach to the opposition and a growing young population without many opportunities.

"It's a creeping unrest," said Ahmed Salim, a Dubai-based East Africa analyst with Teneo Intelligence. He said a lot will depend on how much the government is willing to loosen up its control of industries and whether the country's growth in gross domestic product ends up translating into more jobs.

"The government has enticed a lot of young Ethiopians to come back into the country for jobs that don't exist," Mr. Salim said.

In the last election in 2010 the ruling party won all but two of the legislature's 547 seats. Analysts expect the ruling party to win only about 90% of the seats in Sunday's vote, with the rest going to parties that are friendly to the government. The legislature selects the prime minister, who is the head of the government. The current prime minister is Hailemariam Desalegn, who took over the post after Mr. Meles died in 2012.

The only international observers watching the election are from the African Union after Ethiopia declined to invite the European Union, which monitored the 2010 vote. The EU said in a statement that it also wasn't convinced of the value of sending a team given that previous reports were rejected.

Rana Nour, a doctor who voted Sunday morning in the capital city of Addis Ababa, said she supported the ruling party because of the economic progress she has seen. The Ethiopian government has undertaken major infrastructure projects in recent years, including a light-rail system being built in the capital and a giant dam to increase electricity in the country.

Ms. Nour said that some people felt that they had limited options, but she said she believed the country was moving in the right direction.

"What really is a 100% democracy?" she said. "We are a country trying to install the culture of voting and we are developing our democracy."

Marthe van der Wolf in Addis Ababa, Ethiopia, contributed to this article.

Write to Heidi Vogt at heidi.vogt@wsj.com

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