Cuban President Fidel Castro has applauded Cuban voters for taking part in parliamentary elections.
Fidel Castro voted using a special ballot supplied by election officials
Although the final figure is not clear, officials said turnout had reached 95% with an hour of voting time remaining on Sunday night - despite heavy rains.
The result is a foregone conclusion, with only one candidate for each seat.
The new assembly will meet next month to elect the next president - with the ailing Mr Castro yet to announce whether he wants to remain in the post.
Mr Castro voted by absentee ballot.
"I have done my duty," he announced, adding: "I did not get wet though."
He hailed the number of voters who had turned out "despite the bad weather conditions", reported the state newspaper Granma.
Mr Castro has not been seen in public for almost a year-and-a-half.
His brother, acting leader Raul Castro, said the new chamber would meet on 24 February, when it is expected to decide whether Fidel will remain president.
There were 614 candidates contesting the 614 seats.
Counting of the votes has begun, but the BBC's Michael Voss in Havana says the results are a forgone conclusion.
Voter turnout has always been proclaimed to be more than 95% in previous elections, our correspondent adds.
Raul Castro was the first to cast his ballot when polls near Havana's Plaza of the Revolution opened. He would not say whether his brother planned to remain as head of state or retire permanently.
"We have to face different situations and great decisions," he told Associated Press news agency.
Our correspondent says the vote has been a low-key affair in this one-party state.
But with an ageing leadership, Cuba's Communist Party has encouraged younger people to become involved.
Almost two-thirds of the candidates are standing for the first time, the majority of them under 50 years old.
The new National Assembly has 45 days to meet to select the country's president and a new Council of State.
But Raul Castro, quoted by Spanish news agency Efe, said 24 February had been chosen because it was the anniversary of the proclaiming of the constitution and the beginning of Cuba's 1895 war of independence.
Only then will it become apparent whether 81-year-old Fidel Castro intends to remain as head of state or retire and continue in his current role of elder statesman.