News agencies report that with most of the votes counted, the opposition has won just six of the 75 seats in parliament. A number of opposition members and rights groups claimed the poll was marred by irregularities.
The Organization for Security and Cooperation in Europe (OSCE) is expected to give an initial assessment of the runoff later today. The OSCE said the first round of elections two weeks ago fell short of international standards.
The results are seen as a crucial test of strength both for Akaev and the opposition ahead of October's presidential election. Edil Baislov, head of the pro-democracy Coalition for Democracy and Civic Society, said violations in this round exceeded the number of reported irregularities in the 27 February first round.
"Today on election day we have witnessed very many examples of vote buying," he said. "In several election districts cases of voter transporting were noted. In Khursab District our observers were directly attacked. The case is being investigated. In the second round there are much more serious violations of law."
Central Election Commission Chairman Sulaiman Imanbaev disputed claims of serious violations. He said voter turnout was just over 51 percent.
The elections were held in 40 districts to fill seats still vacant after the initial round of voting. In three other districts voting was postponed until 20 March due to protests that have gripped parts of the country since the first round.
Roza Otunbaeva, the leader of the opposition Ata-Jurt (Fatherland) movement, disputed that claim saying she heard of many "gross irregularities throughout the country." Protests Continue
Ahead of the elections, protesters occupied provincial and local administration buildings in the southern Jalal-Abad and Osh provinces.
Some 2,000 demonstrators in Jalal-Abad rallied for the resignation of President Akaev. They have been there every day since the first-round elections.
RFE/RL's correspondent in the nearby city of Osh reports that about 500 people also attended a protest in that city. Those demonstrators complained about Akaev and his relatives who are candidates for parliament. They also allege fraud during the first-round ballot.
One protester in Osh, Miradil Bakashev, spoke to RFE/RL about what was on the minds of demonstrators.
"Whether this election is held or not, this is not so important to us. Our first and foremost demand is the resignation of President Akaev and early presidential elections. That's because, I would say, this [new] parliament [being elected] will be a pocket legislature -- a family parliament for Akaev," Bakashev said.
For several days last week, demonstrators in the eastern province of Nayrn also blocked a road that links Kyrgyzstan with China. Other demonstrators in the same province made at least two unsuccessful attempts to occupy the provincial administration building.
The wave of political protests in Kyrgyzstan has led some observers to compare the country to other former Soviet republics where popular protests have brought opposition leaders to power.'Yurt Revolution'
Kyrgyz opposition leader Roza Otunbaeva is a former ambassador to the United States and Britain who spoke on 11 March about the comparisons to Georgia's Rose Revolution and Ukraine's Orange Revolution.
But while Otunbaeva accepts that there are similarities, she said events in Kyrgyzstan are different.
"It turned out that there are some peculiarities. The foreigners have been asking us: 'What kind of revolution might there be in Kyrgyzstan? Will it be a rose or tulip one?' Now we say: 'This is the yurt revolution.' People are setting up yurts -- [the traditional felt tents of nomads] -- in different parts [of the country.] I think this shows that people are very ready and active in regions of Kyrgyzstan these days," Otunbaeva said.
Electoral officials banned Otunbaeva from seeking a parliamentary seat when she tried to become a candidate in the current elections. The Central Election Commission cited an election law introduced last year that requires all candidates to reside in Kyrgyzstan for five years before a ballot to be an eligible candidate.
Otunbaeva, who also is a former foreign minister of Kyrgyzstan, had worked for the United Nations in Georgia's region of Abkhazia during two of the last five years.
Had she not been disqualified, Otunbaeva would have been a candidate in the university district of Bishkek.
In fact, today's vote in that district is one of the most-watched runoff ballots. That's because the daughter of President Akaev, Bermet Akaeva, is one of the finalists. The president's daughter also has worked abroad for the United Nations. But Akaeva moved back to Bishkek just more than five years ago.
The voting situation was unclear in the southern Suzak-Bazar-Kurgan District after supporters of a local opposition candidate assaulted a judge on 11 March after he barred the candidate from the runoff election.
(RFE/RL's Kyrgyz Service, AP/Reuters)For more on the Kyrgyz elections, see RFE/RL's dedicated webpage "Kyrgyzstan Votes 2005."