Official results from Venezuela's regional elections show the governing socialist party, Psuv, has won 17 out of 22 governorships - with one still left to count.
Turnout was 61.14 percent in Sunday's polls.
Ballots were cast at 13,559 polling stations nationwide.
The Venezuelan President Nicolas Maduro said it was the highest turnout in 15 years - more than 10 million people voted. Maduro also said the Psuv won 54 percent of the total vote.
Earlier Maduro said the elections had been conducted in a peaceful, exemplary way, "There has not been a single incident, electoral process was perfectly peaceful."
Cuba, Bolivia and Nicaragua, in addition to Honduras, have all sent their congratulations to Venezuela.
The Libre party of Honduras posted a congratulatory letter celebrating the victory of Nicolas Maduro Psuv carrying on Comandante Hugo Chavez movement. The party expressed their solidarity with Chavismo on Twitter.
The Bolivian President, Evo Morales, posted a tweet which said, "Democracy has won over intervention and conspiracy. The people defend their sovereignty and dignity."
Felicitar a Venezuela porque la democracia le ganó a la intervención y a la conspiración. El pueblo defiende su soberanía, dignidad y RRNN.— Evo Morales Ayma (@evoespueblo) 16 October 2017
This is the second election this year in the South American country — the first was held on July 30 to elect members of the National Constituent Assembly, ANC.
Speaking at a news conference, Rodriguez praised the Venezuelan people for going to the polls and ratifying their desire to live in peace. "This was an election convened by the National Constituent Assembly and we were not mistaken," said Rodriguez. "This election has allowed us to consolidate the peace and to defend (our) sovereignty".
She added that the ballot had defeated the opposition's violent agenda and is a lesson from Venezuela to the people of the world.
International guests praised the electoral process for its transparency. The Argentine representative, Pedro Bregier said he and his colleagues had seen no irregularities in the western state of Zulia, an observation echoed by his colleagues around the country
While the Ecuadorean representative of the Council of Electoral Experts of Latin America, CEELA, Alfredo Arevalo said: "It is one of the best electoral processes, audited many times by all parties and political actors."
1.5 percent of voting centers, which had been hit by election-related violence during the ANC vote, had been relocated ahead of Sunday's poll.
The opposition said this was part of a deliberate strategy to discourage people in areas which had traditionally voted for their parties from casting their ballots.
But the government denies this was the case and says that it was to avoid potential threats against voters.
The opposition MUD said they won't recognize the results and are calling for a recount as well as demonstrations on Monday.