The election-date dispute threatens to widen sectarian divisions as Iraqi fighters and US troops, backed by Iraqi National Guard, clash in most of the country's main cities.
A statement by 42 Shia and Turkmen parties, including the influential Dawa Party and the Shia Council for Islamic Revolution in Iraq (SCIRI), said a postponement would be illegal.
SCIRI spokesman Ammar al-Hakim told Aljazeera that the council was in favour of holding the elections as planned on 30 January rather than delaying them.
The Shia statement followed a petition on Friday by 17 political groups calling for a delay of up to six months to ensure the broadest possible participation in the elections.
The parties that backed the petition, drawn up after a meeting on Friday at the house of elder statesman Adnan Pachachi, included the Iraqi National Accord, interim Prime Minister Iyad Allawi's party, and the two main Kurdish parties in the north.
None the less, Allawi's spokesman said on Saturday the prime minister took very seriously his obligation to hold elections by the end of January, as mandated by Iraq's interim constitution and a United Nations Security Council resolution.
But the statement left open the possibility of a postponement.
"The prime minister is aware of the statement made by some parties yesterday, calling for a delay in holding elections," spokesman for the interim government, Thair al-Naqib, said.
"The prime minister understands the concern of these groups, but is equally aware of the determination of others to see elections held on time," al-Naqib added.
The statement said Allawi believed "the key to building real and lasting democracy and stability in Iraq is ensuring all Iraqi citizens can vote".
Allawi's own party is among the
signatories to the poll petition
It added: "He does not believe that a delay will necessarily make such broad participation any easier to achieve."
Several leading political parties have threatened to boycott the elections if they go ahead on time, saying violence in some areas would prevent people from having their voices heard.
A US offensive on areas such as Falluja, Samarra and Ramadi coupled with resistance from various groups has left substantial infrastructural damage, which would make it difficult for voting preparations.
"It is unthinkable that a large and important section of Iraqi society be left out of the political process," Pachachi told a news conference at his Baghdad home on Saturday.
Lack of security
"Security has to improve to enable people to vote without fear, with full security and without intimidation or pressure," Pachachi added.
Iraq's top elections official said on Saturday he alone could not delay the poll, but did not rule out a postponement.
"Legally, to be frank, we don't have that ability," the head of Iraq's electoral commission, Abd al-Husayn Hindawi, said.
Political parties say security and
intimidation are major concerns
He said any delay to the poll would have to be discussed by the electoral commission, interim government, interim parliamentary assembly and the United Nations.
In a statement, the commission said it was still working towards holding elections on 30 January.
One of the major obstacles to gaining wider support for an election delay is the need to convince Ayat Allah Ali al-Sistani, Iraq's leading Shia cleric, who has repeatedly insisted elections must be held as soon as possible.