Final results were not expected until today, but the Central Electoral Commission reported that Medina had 62 per cent of votes with ballots from nearly 60 per cent of polling stations counted. His nearest opponent, businessman Luis Abinader, had 35 per cent.
A senior official in the Medina administration, Jose Ramon Peralta, said on Twitter that the president appeared to have won the highest percentage of the vote in the country's democratic history.
Participation in Sunday's election was about 70 per cent, with voters in the country and at expatriate polling sites in the US and around the world choosing all 222 seats in the Senate and Chamber of Deputies as well as local offices.
Polls going into the election had pointed to Medina as the likely presidential winner. With this victory, the Dominican Liberation Party will have won the four straight presidential elections.
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It appeared the party maintained the control of Congress that it has had for a decade.
Many people had to wait hours to vote, largely because of problems with the deployment of new technology to identify voters by their fingerprints in this country of more than 10 million people.
The electoral commission blamed delays on the resignations of 3,000 technical assistants and other poll workers a day before the election. Replacements had to be trained swiftly. Officials did not disclose why the workers walked off the job before the vote.
He also has drawn support for increased funding for social programs that have strong popular support. Medina's government has built about 2,500 new schools, lengthened the school day to provide more classes and promoted literacy and vocational training for adults.