Hussein al-Shaalan, a senior Iraqiya member, said: "These results keep us in first place, and so we have the right, according to the constitution, to form the government.
"Maybe the calls for a recount in Baghdad were made to prolong the period Maliki remained as head of the government and in a position of strength to negotiate with other blocs," Shaalan said.
However, Iraqiya could still miss out on government after State of Law agreed to unite with another Shia bloc, the Iraqi National Alliance (INA), which took 70 seats in the election.
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Their combined 159-seat total still falls four short of a parliamentary majority, but they would hope to gather the support of a smaller group, probably Kurdish MPs.
Al-Maliki's position has also been strengthened after Saleh al-Obeidi, a spokesman for influential Shia leader Moqtada al-Sadr, told the AFP news agency that his movement would drop a veto against Maliki seeking a new term as long as he met its condition that Sadrist prisoners be freed.
"If he will give us sufficient guarantees to end our reluctance, especially concerning the arrests of Sadrists, then we will not block his candidacy for a second term," he said.
However, al-Obeidi cautioned that Maliki had "not yet succeeded" in meeting the group's demand that around 2,000 of its followers, who were detained on the prime minister's orders, be released.
The Sadrist movement is part of the INA but the the political bloc has a long-running dispute with the premier, who authorised an assault on its armed wing, the Mahdi Army, in 2008.