(Updates Green Zone casualties, death squad victims) By Mariam Karouny BAGHDAD, Jan 25 (Reuters) - At least 34 people were killed in bomb attacks in Baghdad on Thursday but the prime minister said a security crackdown in the capital would leave militants nowhere to hide. In a speech to parliament, Nuri al-Maliki urged politicians on all sides to support his security plan, backed by 17,000 U.S. military reinforcements and seen by many as a last chance to halt sectarian violence in the capital. "There will be no safe haven -- no school, no home, no (Sunni) mosque or Shi'ite mosque. They will all be raided if they are turned into a launch pad for terrorism, even the headquarters of political parties," he said. Maliki said his determination had already borne fruit. "I know that senior criminals have left Baghdad, others have fled the country. This is good, this shows that our message is being taken seriously," he said. Some fear that militants may simply avoid confrontation in the crackdown, betting that eventually U.S. troops will leave. "There is a ... concern they might be lying low, avoiding conflict now in order to fight another day," U.S. ambassador Zalmay Khalilzad said on Wednesday. Criticised for not doing enough about Shi'ite militias linked to some of his allies, Maliki has vowed to take on armed groups regardless of sect or political affiliation. "We have worked hard to get professional officers to lead this plan, with no political affiliations. So let's all help these officers," he said in response to criticism that the army and police were infiltrated by sectarian militias. Washington has identified the Mehdi Army, a militia loyal to radical Shi'ite cleric Moqtada al-Sadr, as the greatest threat to security in Iraq and has warned that the success of Maliki's plan depends on his going after Shi'ite militias with as much determination as he deals with Sunni Arab insurgents. MEHDI ARMY The prime minister, who depends on Sadr's political movement for support in parliament, has been accused of failing to crack down on the Mehdi Army, but officials in his Shi'ite Alliance say he has now accepted he must take action. A senior member of the Sadrist movement, Bahaa al-Araji, pledged the group's support for the plan in parliament, as did the main Sunni Arab and Kurdish parties. The parliament voted unanimously to support the plan. Since Maliki announced his plan earlier this month there has been a series of bombings and dozens of bodies are still found dumped in the city on a daily basis, apparent victims of death squads. Thirty-three were found on Wednesday alone. A car bomb ripped through a shopping district in Karrada in central Baghdad, killing 26 people and wounding 64, a police source said. Another car bomb and a motorcycle bomb exploded in other markets, killing five people, while a roadside bomb killed three, police said. Two rockets landed in the heavily fortified Green Zone housing the government and embassies, provoking loudspeaker warnings to people to take cover. The U.S. military said six people were hurt. Maliki said Iraqi security forces would start to remove squatters from Baghdad homes they have illegally occupied since the owners fled sectarian violence. "Today or tomorrow we will start arresting those who are living in the homes of refugees, to open the way for their return," he said. Tens of thousands of people, including Shi'ites, Sunni Arabs and Christians, have fled Baghdad, where violence and intimidation have turned many mixed districts into sectarian enclaves. Maliki rejected suggestions his security plan was a last chance: "The battle between us and terrorism is an open-ended battle. It does not stop with the end of this plan." White House spokesman Tony Snow welcomed Maliki's speech as "a very assertive address", adding: "We certainly welcome that because it demonstrates the kind of vigour that we've been talking about and that the American people expect."