However, Zenawi denied the accusations, and said residents were free to vote as they pleased.
'Peaceful and calm'
Observers from the European Union confirmed there were some allegations of irregularities that they said still needed to be evaluated. But the EU observer mission said the parliamentary vote had mostly been "peaceful and calm".
"In the vast majority of polling stations, the elections were well organised," Thijs Berman, the EU's chief observer, said.
He said that half way through the election day, turnout was already 70 per cent.
"With this very high turnout and this peaceful and calm election, Ethiopians have shown that they want full respect of their democratic rights, full respect of their electoral laws."
Some 32 million Ethiopians - 90 per cent of eligible voters - were expected to cast their ballots at more than 43,000 polling stations across the country on Sunday.
Al Jazeera's Andrew Simmons, reporting from the capital Addis Ababa, said most people were wondering by what margin the ruling Ethiopian People's Revolutionary Democratic Front (EPRDF) would win, rather than whether it would win.
The EPRDF's biggest challenge comes from the eight-party coalition Medrek - or the Forum - but it is united chiefly by its desire to unseat Meles and has not set out clear policies, our correspondent said.
The opposition admits that it has little chance of victory but says that is because the EPRDF has tightened its grip on power since the 2005 polls, routinely intimidates and jails its critics and tries to divide the opposition.
Meles became leader of Ethiopia in 1991 when an armed group led by him ousted a communist government that killed hundreds of thousands of Ethiopians in a 17-year rule.
He was lionised by the West in 1991, with the then US president, Bill Clinton, calling him one of a "new generation" of leaders who would bring democracy to the continent.
But Meles, 55, has increasingly been criticised by rights groups, who say he is becoming more autocratic and stifles dissent in the country of 80 million people.
Birtukan Mideksa, leader of one of the Medrek member parties and seen by analysts as a potential replacement for Meles, is in prison accused of violating the terms of a pardon that released her from a previous jail spell in 2007.
Medrek is running 421 candidates for the 547-seat federal parliament, not as high as the EPRDF's 521, but enough to form a clear majority should they pull off a shock win.
The next biggest opposition parties, the All Ethiopian Unity Organisation and the Ethiopian Democratic Party are running 350 and 250 candidates respectively.