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. 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. 