Iraq celebrated the withdrawal of American troops from its cities with parades, fireworks and a national holiday as the prime minister trumpeted the country's sovereignty from American occupation to a wary public. Even with a deadly car bombing and other mayhem marring the day -- the deadline for the American troop pullback under a Jan. 1 agreement -- Prime Minister Nouri Kamal al-Maliki seized on the occasion to position himself as a proud leader of a country independent at last, looking ahead to the next milestone of parliamentary elections in January. He made no mention of American troops in a nationally televised speech, even though nearly 130,000 remain in the country; most had already pulled back from Iraq's cities before Tuesday's deadline. The excitement, however, has rung hollow for many Iraqis, who fear that their country's security forces are not ready to stand alone and who see the government's claims of independence as overblown. From Basra in the south to Mosul in the north, Iraqis expressed skepticism about the proclamation of 'independence.' 'They will not withdraw to their homes; they will stay here and there so that they can return in emergencies,' said Samir Alwan, 28, the owner of a mini-market in Basra. 'So it is not sovereignty, according to my point of view, and I think that the Iraqi army is only able to secure the south of the country and unable to secure Baghdad and Mosul.' In a national address, al-Maliki focused his praise on Iraqi troops and security forces for their role in fighting the insurgency. 'The national united government succeeded in putting down the sectarian war that was threatening the unity and the sovereignty of Iraq,' he said, as if the United States had played no role. President Barack Obama, who ran for office on a pledge to end the war, marked the occasion with minimal fanfare, declaring it 'an important milestone' even as he warned of 'difficult days ahead.' 'The Iraqi people are rightly treating this day as cause for celebration,' he said. The withdrawal did not command its own presidential appearance -- his brief remarks were delivered at a ceremony honoring entrepreneurs -- a marked contrast with his predecessor, who rarely missed an opportunity to celebrate milestones in Iraq. Underscoring the insecurity, a suicide bombing in a market in a Kurdish neighborhood in the volatile northern city of Kirkuk near dusk killed 33 people, according to police there. In Baghdad, the American military reported that four U.S. soldiers had been killed in an attack on Monday, a number higher than usual, underscoring the vulnerability of the troops as they withdraw. Military experts anticipate more violence in the days ahead. Maliki's effort to capitalize on Iraq's latent anti-Americanism and to extol the abilities of his troops is a risky strategy. If it turns out that Iraqi troops cannot control the violence, al-Maliki will be vulnerable to criticism from rivals -- both if he has to ask the Americans to return but also if he fails to enforce security without them. Some American commanders have said they were taken aback by al-Maliki's insistence on taking credit for all the security successes in Iraq, but they also see the importance of having him and Iraqi troops appear strong, especially in the face of multiple insurgent factions intent on destabilizing the government. Gen. Raymond T. Odierno brushed aside the dismissive tone of Iraqi leaders' public remarks about the Americans, saying that al-Maliki had personally thanked him on Monday night and again on Tuesday for the sacrifices American troops have made. 'I do not get these negative comments from the political leaders that are in the government,' he said at a press conference at the American military headquarters at Camp Victory. 'In my mind, I frankly don't worry about those comments because I understand that we are working this together.' He also played down concerns about security in Iraq's cities after the withdrawal of most American combat forces, noting that nearly 130,000 troops still remained in Iraq. He said that the American and Iraqi militaries continued to cooperate on security issues inside and outside the cities. In most places the transition to the Iraqi forces has gone relatively smoothly but there have been unpleasant bumps, reminders of the underlying tensions between the two militaries and the resentment that American soldiers feel as the Iraqis appear eager to push them out the door even though they still want them to be on call. In Diyala, where the Americans closed 11 of 18 bases or outposts ahead of Tuesday's deadline, the transfers have not gone entirely smoothly. An official in al-Maliki's office showed up early at a camp near Baqouba and complained that the Americans had not left behind generators and air conditioners for the Iraqis -- something that the American commander in the region said had never been part of the agreement. The dispute on Sunday delayed the formal handover. 'You can't treat your partners that way,' the commander, Col. Burt K. Thompson of the 1st Stryker Brigade, 25th Infantry Division, said in Baqouba. For Iraqis, claiming sovereignty is something of a national pastime, with various politicians celebrating different markers: 2004, when the American-led Coalition Provisional Authority handed power to the interim Iraqi government; 2006, when Iraq seated its first constitutionally elected parliament; and Jan. 1, when the security agreement went into effect. Al-Maliki seems to be making a conscious effort to cement his image as a strong ruler by using many of the same tools of power as the predecessor he hated so much, Saddam Hussein. He has used the state television network and newspaper to broadcast nationalist messages, and parades and festivals to encourage an outpouring of public pride. Over the past several days the state television network, Iraqiya, not only ran a 'Countdown to Sovereignty' clock but also aired promotional spots glorifying Iraqi history, culture and people. Its frames of the marshes of southern Iraq, the markets of Baghdad, men performing traditional dances and children playing in the mountain meadows of Kurdistan -- much of it footage filmed before the 2003 invasion --presented an image of Iraq completely unfamiliar to most Iraqis, who now live in neighborhoods cordoned off by blast walls and are forced to go through multiple checkpoints everyday. 'This is all for the media,' said Amina al-Esadi, a female searcher at the compound of the Islamic Supreme Council of Iraq, a religious Shiite political party. 'Some people are afraid because the Americans have left. Some think it will be better because then the enemies of the Americans will leave Iraq' and the country will be safer, she said. 