The twin setbacks for authorities, grappling with Iraq's worst period of unrest since the country emerged from a sectarian war that killed tens of thousands, come just months before parliamentary elections.
UN chief Ban Ki-moon and other diplomats have urged Iraq's leaders to seek political reconciliation to resolve nationwide violence and the standoff in Anbar, but Prime Minister Nuri al-Maliki has ruled out dialogue with militants as his forces have launched wide-ranging security operations.
Eight car bombs hit civilian targets in majority-Shiite or confessionally mixed neighbourhoods of the capital, killing 27. One of them targeted a packed market in the neighbourhood of Shaab.
Another detonated outside a restaurant on Sanaa Street, killing three people and badly damaging the restaurant and nearby shops and cars, an AFP journalist said.
Also Read
Windows of nearby shops were shattered, the restaurant's ceiling partially caved in and blood and mangled vehicle parts were scattered around the scene.
A suicide bombing at a funeral in Buhruz, in restive and religiously mixed Diyala province north of Baghdad, killed 16 people and wounded 20, officials said.
The funeral was for a member of the Sahwa, the Sunni tribal militias who sided with the US military from 2006 against their co-religionists in Al-Qaeda, helping turn the tide of Iraq's violent insurgency.
As a result, they are often targeted by Sunni militants who see them as traitors.
Seven others, including three soldiers, were killed in and around the northern city of Mosul.