Zenawi has ruled Ethopia since 1991 when he came to power in a military coup.
"The process of the elections was not democratic-building but was a regression in democracy," Shawel said.
"It is unclear whether or not this call for new elections will change anything," Andrew Simmons, Al Jazeera's correspondent in Addis Abba, the Ethiopian capital, said.
Shawel's call for fresh elections came a day after European Union election observers said the election was held in "a narrowing political space" that favoured the ruling party.
Human Rights Watch criticised Sunday's vote as corrupted by pre-election irregularities, including telling voters they could lose food assistance, public-sector jobs, loans and educational opportunities if they voted against the ruling
Ethiopian People's Revolutionary Democratic Front (EPRDF).
According to provisional results, the EPRDF and allies had scored a landslide victory, winning an overwhelming number of votes in nine out of 11 regions and cities declared so far.
Meanwhile, Mike Hammer, a spokesman for the US National Security Council, has said that US embassy officials were denied accreditation and the opportunity to travel outside of the capital to observe voting.
"The limitation of independent observation and the harassment of independent media representatives are deeply troubling," he said in a statement.