World leaders have welcomed the formation of the first full-term Iraqi government since the 2003 invasion.
Mr Maliki set out a 34-point government programme
US President George W Bush said the future was a great challenge but there was an "opportunity for progress".
The cabinet unites members of the major Shia, Kurd and Sunni parties and is to hold its first meeting on Sunday.
Three crucial ministries - national security, interior and defence - have still to be agreed but new PM Nouri Maliki vowed to heal sectarian strife.
In a keynote speech Mr Maliki said Iraqis must "denounce terrorism" and find an "objective timetable" for international forces to leave.
He told parliament that Iraqis needed to unite in a spirit of love and tolerance and "close up divisions that have emerged through sectarianism".
Mr Maliki laid out a 34-point government programme that included tackling terrorism, integrating militias into the security structure and getting electricity and water back on line.
US President George W Bush said Iraq's transition to full government had been "difficult and inspiring".
"This broadly representative unity government offers a new opportunity for progress in Iraq," he said in a White House statement.
He said the new leaders faced great challenges but "they also know that they - and their great country - will not face them alone".
British Prime Minister Tony Blair described the move as a huge step forward and Arab League Secretary-General Amr Moussa called it a "step on the right path".
Jordan's King Abdullah II said he hoped the move would "fulfil the aspirations of [Iraq's] people for a better life, democracy, pluralism and stronger national unity".
IRAQI CABINET - KEY POSTS
PM & acting interior minister - Nouri Maliki, Shia
Deputy PM & acting defence minister - Salam Zaubai, Sunni
Oil minister - Hussain al-Shahristani, Shia, ex-deputy parliamentary speaker
Foreign minister - Hoshiyar Zebari, Kurd. Held post since 2003
Finance minister - Bayan Jabor, Shia, former interior minister
However, the BBC's Jim Muir in Baghdad says the new unity government got off to a messy start.
Before Mr Maliki could begin announcing his team, the leader of the Dialogue party - the smaller of the two main Sunni factions - seized the microphone to complain about how negotiations over the distribution of roles had been conducted.
Once Mr Maliki was able to speak, members of the 275-seat parliament - the Council of Representatives - applauded as each new member of the Cabinet was named and took their seat.
But then a member of the biggest Sunni faction, which is included in the government, angry about the defence and interior ministry roles being left open, led a walk-out.
Mr Maliki will for now run the interior ministry and Deputy Prime Minister Salam Zaubai, a Sunni, will run defence.
With security the key issue, BBC defence correspondent, Rob Watson, says in the short term the new government is unlikely to affect what is a complex breakdown of law and order, involving Sunni insurgent groups, Shia militias and mafia-style criminality.
A blast in Sadr City, Baghdad, was a warning of continued violence
Just hours before the parliament began its session, at least 19 people were killed and 58 wounded in a bomb attack in the Shia district of Sadr City in the Iraqi capital, Baghdad.
Sectarian violence has spiralled in recent months. The latest cycle of attacks began with the bombing in February of a Shia shrine in the town of Samarra.
It was followed by the regular reports of the discovery of dumped bodies, bearing marks of torture and execution.
Sunni politicians said Shia death squads operating within the security forces were behind the killings.
The new unity government is the result of five months of arduous negotiations, following December's general elections, in which the Shia alliance emerged as the largest single bloc.
It is the first to include the main Sunni Muslim factions, which had boycotted the interim elections and cabinet.