Giving Sunnis a greater stake in power could help encourage them to join a counter-offensive against the jihadists.
New UN human rights chief Prince Zeid Ra'ad Al Hussein said the atrocities IS had committed in areas under its control had shown Sunnis that jihadist rule promised only a "house of blood", while the head of Egypt's prestigious Al-Azhar religious institution also condemned the group.
The key parliament session opened with speaker Salim al-Juburi struggling to maintain order and many MPs absent, but a total of 289 out of 328 eventually turned up.
- Key posts unfilled -
MPs approved three deputy prime ministers and 21 ministers in individual votes on Monday, but the key interior and defence posts and others remain empty.
Abadi has asked for a week to fill them, during which time he will run the ministries in an acting capacity.
The previous government also began with various posts unfilled, and acting ministers served for the next four years.
The oil ministry went to former vice president Adel Abdel Mahdi, the foreign ministry to former prime minister Ibrahim al-Jaafari, and finance to former deputy premier Roz Nuri Shaways.
Saleh al-Mutlak will continue as deputy prime minister, while the other two deputy premier posts went to ex-foreign minister Hoshyar Zebari and MP Baha al-Araji.
The cabinet so far runs heavily to Shiite Arabs, who make up the majority of Iraq's population, and includes only one woman.
Parliament also approved three fierce rivals as the country's new vice presidents: former premiers Nuri al-Maliki and Iyad Allawi, and ex-parliament speaker Osama al-Nujaifi.
The participation of Iraq's Kurds -- who have a three-province autonomous region that is at odds with Baghdad over issues including territory and division of the country's vast natural resources -- was agreed only at the last minute.
Kurdish leaders met in the northern city of Sulaimaniyah to discuss whether to take part in the government, but their MPs had apparently not received the final word when parliament opened and were waiting in the cafeteria.
They later arrived in the chamber, and Kurdish MP Ala Talabani announced during the session that the Kurds would participate in the government on a three-month trial period.
In remarks to parliament outlining his proposed programme, Abadi said that "my government is committed to solve all suspended issues with the Kurdistan Regional Government".
Of the cabinet-level posts agreed Monday, the Kurds received two ministries and a deputy premiership.
- Kerry heading to region -
US President Barack Obama, who made his political career opposing the war in Iraq and pulled out American troops in 2011, promised to unveil a long-awaited strategy on Wednesday to tackle IS in both Iraq and neighbouring Syria.
"We are going to systematically degrade their capabilities. We're going to shrink the territory that they control. And ultimately we're going to defeat them," Obama said in an interview aired Sunday on NBC's "Meet the Press".
He said he would not announce the return of US ground troops to Iraq and would focus instead on a "counter-terrorism campaign".
Secretary of State John Kerry was to leave the United States on Tuesday on a trip to Jordan and Saudi Arabia as part of efforts to build an international coalition to counter the IS militants.
A State Department spokeswoman said that more than 40 countries have already indicated a willingness to help out in some way against the jihadists.
- 'House of blood' -
Prince Zeid, the first Muslim and Arab to serve as UN High Commissioner for Human Rights, said that IS had already shown the world what its rule would be like if it was left unchecked.
"It would be a harsh, mean-spirited house of blood," he said in his maiden speech to the UN Human Rights Council. IS "has demonstrated absolute and deliberate disregard for human rights".
The bloodshed continued on Monday when gunmen and suicide bombers attacked the town of Dhuluiyah, north of Baghdad, killing 18 people, police and a doctor said.
Sheikh Ahmed al-Tayyeb, the head of Egypt's Al-Azhar, Sunni Islam's highest seat of learning, also sharply criticised IS jihadists, calling them "criminals" transmitting a "tarnished and alarming image of Muslims".
Washington expanded its air strikes to the Sunni Arab heartland over the weekend, hitting IS targets around a key dam on the Euphrates that troops have been battling to defend with the support of allied tribes.