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Venezuela's ruling party has won 20 out of 23 state governorships in regional elections, the first in four years in which the main opposition parties took part, official results show.
Opposition candidates only won three governor's posts in Sunday's poll. Turnout was low at 41.8%.
Cuba congratulated Venezuelan President Nicolás Maduro, a close ally, before the results were announced.
The US said the elections were not free and fair.
"Fearful of the voice and vote of Venezuelans, the regime grossly skewed the process to determine the result of this election long before any ballots had been cast," US Secretary of State Antony Blinken said.
"Maduro robs Venezuelans of their chance to shape their own future," he said.
No boycott but low turnout
The election was the first in nearly four years which was not boycotted by Venezuela's main opposition parties.
In previous elections, these parties had told their voters to refrain from casting their ballots arguing that it was not a fair contest.
The election which saw Mr Maduro re-elected as president in 2018 was marred by vote-rigging claims and more than 50 countries refused to recognise him as Venezuela's legitimate leader.
But with Mr Maduro still in the presidential palace and the European Union sending electoral observers, the main opposition parties decided to change strategy and take part in Sunday's polls.
However, many opposition voters questioned this move, arguing that the Socialist party - which has been in power for the past 22 years - has developed such a tight grip over the electoral authorities and other institutions that free elections are not possible.
Preliminary results suggest the opposition did not manage to dispel the distrust many Venezuelans had in the voting process.
The opposition only won in the states of Zulia, Nueva Esparta and Cojedes, while government-allied candidates swept to power in the remaining 20, according to preliminary results.
And while a government victory was widely anticipated in most states, many Venezuelans commented on a tweet by Cuban President Miguel Díaz-Canel, who congratulated his ally, Mr Maduro, on the "convincing victory" even before Venezuela's electoral authorities had announced the first results.
Analysts said apathy also contributed to the low turnout with many voters worn down by Venezuela's deep economic crisis.
Three out of four Venezuelans are living in extreme poverty, according to a national survey.
Government-critical media reported that some voters had been intimidated by members of violent pro-government gangs, but the National Electoral Council said that there had only been "small and isolated problems".
The EU electoral observer mission is due to present its report on the election on Tuesday.