The first bomb exploded outside a police academy on Sunday in the hometown of ousted president Saddam Hussein just after 8am (0410 GMT) as recruits were preparing to travel to Jordan for training, police colonel Abd Allah Ali said.
The second blew up 20 minutes later outside a nearby army liaison office.
"We have received the bodies of six dead and 26 wounded," Raad Tikriti, a doctor at the local hospital, said.
Police casualties included four dead and 18 wounded, said Ali.
The governing coalition in Iraq has run into fresh problems, with the main Sunni Arab alliance demanding eight posts in the new cabinet, including that of a deputy premiership and a key ministry.
On Saturday, The National Front acknowledged mounting public frustration at the slow pace of talks and called for a meeting of all parties within 24 hours to thrash out a final agreement.
Referring to what it described as the "regrettable delay in forming a government" 12 weeks after the landmark elections, the group called for a meeting within 24 hours between all parties concerned in order to solve the problem.
Iraq's new president, former Kurd rebel leader Jalal Talabani, voiced his exasperation on Friday. "I'm frustrated with the delay in forming the government," he said.
The 30-plus parties within the National Front, most of them without representation in parliament after the widespread boycott of January's election by the Sunni Arab minority, met on Saturday after talks the previous day with Talabani.
Allawi called for safeguarding
Iraq's attempts at democracy
The Shia-led United Iraqi Alliance took 146 of the 275 seats in parliament, while the main Kurdish bloc took 77. But both groups want to include the Sunni Arabs in a new government in an effort to wean the former elite away from anti-US fighters and into the political mainstream.
Blame for delay
Meanwhile, the deputy secretary-general of the Iraq's Unified Council (IUC), Muhammad Shihab al-Dulaymi, denied that the Sunni Muslims were responsible for the delay in government formation.
"Sunni Arabs are not to blame for any delay in forming the government; only stubborn groups have to be blamed," he told Aljazeera from Baghdad.
"We, in the IUC, have contributed greatly to the Front of National Groups, but it seems the groups who won the elections want to give only marginal posts to the national parties that have not participated in the electoral process," he said.
He said the posts offered to the Sunni Arabs did not do justice to the demographic representation of the group.
Al-Dulaymi said the IUC had asked for the defence ministry and seven other ministries.
He said it was agreed that Sunnis should get the post of the deputy prime minister.
If the cabinet is not appointed by early next month, interim Prime Minister Ibrahim al-Jafari could be forced to step down.
On Saturday, Iyad Allawi, Iraq's outgoing prime minister, urged the legislators to "safeguard Iraq's march toward democracy" by ending the standoff.
Iraqi UN envoy Ashraf Qazi travelled to Baghdad on Thursday to meet al-Jafari and urge him to end the delay and include all parties in the new government so it can soon begin the difficult process of writing a new constitution.
"Some Kurds are holding up al-Jafari's efforts to form a government so the deadline will expire and another prime minister will have to be selected"
a member of the Shia alliance
The standofff is blamed largely on two things: Kurdish factions that oppose al-Jafari, a Shia Arab leader, as prime minister; and Shia factions that do not want ministers selected from Allawi's secular party.
Al-Jafari's Islamic Dawa Party, a major group in the Shia-led United Iraqi Alliance, has close ties with Iran's religious leaders and with Iraq's most influential Shia cleric Grand Ayat Allah Ali al-Sistani.
Some Kurdish legislators want a more secular prime minister and one who favours a federal government that would give strong autonomy to Iraq's Kurdish north.
In a telephone interview on Saturday, Sami al-Askari, a member of the Shia alliance, said some Kurds distrust al-Jafari so much they want to delay the formation of the cabinet in an effort to unseat him.
"Some Kurds are holding up al-Jafari's efforts to form a government so the deadline will expire and another prime minister will have to be selected," al-Askari said. Another Shia official confirmed that, speaking on condition of anonymity because the negotiations are ongoing.