The NDP deplored Wafd's decision to boycott Sunday's run-off.
"Wafd's lame justifications for withdrawal reflect the trauma the party has experienced," the ruling party said in a statement on Thursday.
Wafd leader Al-Sayyed Al-Baddawi had said earlier that his party "will not be partners in forgery."
Hamzawi said the government would be unhappy about its sweeping success.
"They would have liked to keep a 70-percent majority and to keep the opposition to 20 percent. But they changed the centre of gravity from the Brotherhood to Wafd."
Hamzawi said the way the vote was conducted "had taken Egypt back to before the 1970s" when there was no effective opposition.
The election, seen as a forerunner to the crucial 2011 presidential vote, was heavily criticised by Egypt's ally the United States and by human rights groups, especially for the harassment and intimidation of the Islamists.
"It's bad for the reputation of the presidential election, which needs a legitimate parliament and other candidates," Hamzawi said.
The Brotherhood, the only serious opposition force in the country, controlled a fifth of the outgoing parliament, but did not win any seats outright in Sunday's first round of voting.
Wafd secretary general Munir Fakhir Abdel Nur told AFP his party would give up the two seats it won in the first round.
The Islamist Brotherhood had fielded 130 candidates, who register as independents to get round a ban on religious parties. More than a dozen were disqualified and at least 1,200 supporters arrested.
By contrast, the NDP fielded about 800 candidates, many of them competing for the same seat.
Observers say the NDP's decision to have more than one candidate contesting the same seat was a sign of weakness within the ruling party.
"They have not been able to operate in the election like a real political party," said a Western diplomat in Cairo who spoke on condition of anonymity.
"They have not been able to get people behind any particular party platform. They have not been able to impose any party discipline, although it seems this year that they did try very hard."
Senior NDP official Ahmed Ezz said opinion polls the party conducted before the vote showed the Brotherhood had marginal support in districts supposed to be Islamist strongholds.
"Whoever understands what the prelude was would not have been surprised by the results," said Ezz.
He added "the headline for Sunday should be: 'How the NDP brought down the illegal organisation'," the government's euphemism for the Brotherhood.
Egypt's independent press on Thursday continued to decry Sunday's electoral violations and the way the government has tightened its grip on power.
"What happened in the first round confirms that the ruling party is determined to completely monopolise power, even if it must resort to fraud," said columnist Hassan Nafaa, writing in the independent daily Al-Masri Al-Yom.
Nafaa said the repression of the opposition seemed to be a step towards confirming Mubarak's son Gamal, who heads the NDP's policy committee, as the party's official presidential candidate.
The 82-year-old president, who has yet to say whether he will stand for a sixth term in office, is widely believed to be grooming Gamal for succession.
"As an indication of weakness in the party you could come to the conclusion that the NDP itself will be much less effective in terms of being a vehicle or a voice for the succession in Egypt," the Western diplomat said.