According to Iraq’s Alahed TV, Fatah (Conquest) Alliance has won six more seats to reach a total of 20.
The block of Iraqi cleric Muqtada Sadr is still sitting top of the table but its seats has decreased from 73 to 70.
The State of Law Alliance, headed by former Prime Minister Nouri al-Maliki, who led Iraq from 2006 to 2014, has added three more seats to the earlier announced 37.
Iraqi officials say the results are subject to change and not final yet as the counting continues.
Earlier on Tuesday, Hadi al-Amiri, leader of Iraq's Fatah (Conquest) Alliance political coalition had dismissed the preliminary results as fabricated. “We will not accept these fabricated results, whatever the cost,” the Arabic-language al-Sumaria television network quoted him as saying, PressTV reported.
“We will defend the votes cast for our candidates and voters with full force.”
Separately, the Coordinating Committee of Shia Parties in Iraq rejected the results of the national elections, and raised strong objection over what it described as the High Electoral Commission’s failure to honor its obligations.
The committee is comprised of Fatah Alliance, the State of Law Alliance, Asa'ib Ahl al-Haq political party, Kata'ib Hezbollah as well as other Shia factions.
A count based on initial results from several provinces plus the capital Baghdad, verified by local government officials, suggested that Sairoon coalition led by influential Shia Muslim scholar Muqtada al-Sadr had won more than 70 seats, which if confirmed could give him considerable influence in forming a government.
Kurdish parties won 61 seats, the results showed, including 32 for the Kurdistan Democratic Party which dominates the government of the semi-autonomous Kurdish region of Iraq, and 15 for its rival the Patriotic Union of Kurdistan party.
Sunni parliament speaker Mohammed al-Halbousi's Taqaddum coalition won 38 seats, Iraq's state news agency reported, making it the second largest in parliament.