(CNN) -- Hours after insurgents killed dozens of people on Tuesday in a new wave of bomb attacks in Baghdad, former Iraqi Prime Minister Ayad Allawi said he hopes to soon form a new government after claiming victory in the March 7 ballot.
"We need the (election) results to be officially announced by the Supreme Court, and then I guess it will take us in the range of two months to form ... I hope to form ... a government," Allawi told CNN's Christiane Amanpour.
Allawi said he believes his Iraqiya bloc, which has a narrow two-seat lead in parliament over his main rival, has the right to form the next government under the country's constitution. Iraqiya won 91 seats and current Prime Minister Nuri al-Maliki's State of the Law coalition won 89 seats, according to the provisional election results.
"We can't just have a national unity government, a government which has been stagnant as the current government has been," he said. "We need to have a government that can function and can provide, especially for the security of this country."
His comments came amid new concerns that security in Iraq is beginning to unravel in what many say is a political vacuum following the elections.
Insurgents exploded at least seven bombs in Baghdad on Tuesday, killing more than 30 people and wounding 140 others. It was the latest in a series of attacks that have killed more than 100 people in five days.
"I expected this violence, especially after the elections, because there is a vacuum, and there is indeed a constitutional vacuum at this time," Allawi said. "And indeed the terrorists and groups who are linked to terrorism would find the political environment useful for them to start damaging and inflicting more damage on the Iraqi people."
Former U.S. National Security Council official Brett McGurk said Iraq has not seen any signposts of real deterioration despite the upsurge in violence.
"We haven't seen militias take to the streets to protect neighborhoods," he said. "We've not seen the ministries stand down, things we started to see in 2006."
Allawi said the success of his bloc in the elections showed that the Iraqi people were fed up with sectarianism.
"They want to see a secular country with a professional, functional government, and they want to get out of the bottleneck that we are in now," he said.
He rejected the arguments of critics who say Allawi's bloc is a front organization for former Baathists who served in the Saddam Hussein regime.
"The Baath .. are finished. It's ended. We are in a new era," he said.
Allawi said he was talking to other political parties about the formation of a new government coalition -- including supporters of the influential Shiite cleric Muqtada al-Sadr, whose followers won some 40 seats in parliament.
"The Sadrists are welcome to join it," he said. "We are talking to them already. And the discussions are progressing well."
Allawi said there was a big difference between political supporters of al-Sadr and its once powerful Jaish al-Mahdi militia.
The former U.S. Ambassador to Iraq, Ryan Crocker, said he was not concerned about the potential role of al-Sadr's supporters in a coalition government.
Crocker said: "The Sadrists have always had an appeal to the dispossessed urban Shia populations, and they finally found a way to get their act together sufficiently to garner a respectable number of seats."
"But clearly they are not going to form a government," he said. "They may be instrumental in the government's formation, but they're going to have to be part of the give-and-take of Iraqi politics as well."
Crocker, however, said he believed Allawi was being overly optimistic when he said he could form a government in two months.
"I think a more realistic deadline is the beginning of Ramadan at the start of August," Crocker said. "So I worry about a decision to have us down to 50,000 (American) troops perhaps in the same month that a new government is formed."
Crocker was referring to the planned withdrawal of all U.S. combat troops from Iraq by the end of August, leaving a residual force of 50,000 troops until a final U.S. withdrawal scheduled for the end of 2011.