The United Iraqi Alliance (UIA) said it was willing to talk with Sunni and secular politicians about their participation in Iraq's new government.
Friday saw thousands of Sunnis protest over what they said was vote fraud.
Preliminary results suggest that the Shia group has won a majority, but will still need to form a coalition to select a president and prime minister.
Meanwhile, Iraq's electoral commission has struck off 100 election candidates for having links with Saddam Hussein's banned Baath party.
Iraq's Electoral Commission has registered more than 1,000 complaints of election irregularities, and correspondents say a few dozen of them are considered serious enough to have affected the final distribution of seats in parliament.
The UIA said that the complaints of fraud had come from many different sectors, and did not only affect the minority parties.
"There will be no retreat and no rerun of the election," said Jawad al-Maliki, a senior member of one of the main parties in the UIA.
"In the end, we have to accept the results and the will of the people," he told a news conference.
He said negotiations had already begun to form a "broad-based national unity government".
But he added: "Some of those who have been shocked by their defeat and by the great results realised by the winning slates insist on making trouble."
Negotiations over the shape of the new government are expected to take weeks, if not months.
Shias Reject Iraq Election Re-run
Iraq's main Shia coalition party has called on Sunni Arabs to end demands for a re-run of the parliamentary poll.