William Lara, a leading lawmaker in Chavez's governing party, said internal tallies of the Fifth Republic Movement indicated pro-Chavez candidates could sweep all 167 of the assembly's seats.
Chavez earlier dismissed the boycott as a failed ploy to sabotage legitimate elections and avoid an embarrassing defeat, and officials later blamed a pipeline explosion on government opponents.
"The whole world knows a true democracy is in motion here in Venezuela," Chavez said after voting at a school where cheering supporters greeted him outside.
Chavez accused the United States, with which he often clashes, of being behind the boycott — a charge Washington has denied.
The boycotting parties said they did not trust the voting system. Chavez said Venezuela has the most solid electoral system in South America, and that its integrity was secure despite "attempts to sabotage this process."
Officials and election observers said the voting proceeded peacefully Sunday, while thousands of soldiers were deployed to keep order. The military said it stepped up security at oil installations to prevent any possible sabotage in the country, the world's No. 5 oil exporter.
Government officials reported several disturbances leading up to the vote, including blasts from small explosives that injured three people in Caracas on Friday and a pipeline explosion Saturday night in the western state of Zulia.
Interior Minister Jesse Chacon said C-4 explosives were used to blow up the pipeline and that officials believed the perpetrators were government opponents trying to destabilize the country.
"We already know who is behind this situation, and we have made some detentions," Chacon said, without giving details.
Chavez said the situation in the country was calm and that such acts had no effect on the voting process.
Oil Minister Rafael Ramirez blamed the same opponents who unsuccessfully tried to oust Chavez in a two-month strike that ended in early 2003. Ramirez said a gas pipeline running along the same route was also attacked, but that there was no damage.
Chavez said traditional parties that withdrew would be responsible for their own demise, and he cited electoral figures showing that only 556 of more than 5,500 candidates had quit the race.
"They are old parties that are already dead," Chavez said. He added that boycotting parties could emerge "not only delegitimized but also illegal." He did not elaborate.
Candidates allied with Chavez hold 89 of the National Assembly's 165 seats and are aiming to increase their majority in an expanded 167-member congress. If they win a two-thirds majority, some pro-Chavez lawmakers have said they would consider changing the constitution to extend term limits for all offices, including the president.
Chavez said any constitutional changes would have to be considered later, and that the choice would not be up to him.
Chavez supporters called the boycott a desperate stunt by an opposition that polls predicted would have soundly lost.
"If they really are democrats, they should be participating," said Jesus Acosta, a 47-year-old accountant who waited in line to cast his ballot outside a school.
The boycotting parties argue the National Electoral Council is pro-Chavez, there are irregularities with the voter registry and the touchscreen voting machines are vulnerable to confidentiality breaches.
Julio Borges, an opposition presidential candidate whose Justice First party was boycotting, called it a sad day and said his party hoped to eventually achieve "total confidence" in the electoral system.
The Organization of American States, which has 60 observers monitoring the vote, said last week that "important advances" had been made to generate confidence in the elections. The European Union has an additional 160 observers on hand.
Chavez was elected in 1998 promising a revolution for the country's poor and is up for re-election next year. His enemies tried to overthrow him in a short-lived 2002 coup, backed the crippling oil strike that died out in early 2003 and organized a failed recall referendum last year.
Nuvia Castro, a nurse, said she was abstaining to make a statement against what she sees as Chavez's increasing grip on power.
"If we vote, they'll say they won," she said. "When the rules are clear, we'll decide to vote."