None of the attacks has been claimed but Washington has repeatedly blamed Iran-backed military factions in Iraq.
The high praise from the right stood in stark contrast to reaction from Democrats, who severely criticised Trump's latest move.
US Secretary of State Mike Pompeo said the attack was "orchestrated by terrorists."
Baghdad said it would summon the US ambassador while Washington responded by accusing Iraqi authorities of having failed to "protect" US interests.
The attack happened in an area around Tayran Square, which is usually crowded by labourers seeking work.
Iraq's interior minister Qasim al-Araji has said agents from his country have infiltrated Isis sleeper cells to prevent further bomb attacks.
Companies allege Baghdad is employing strong-arm taxation tactics to extort more money.
Karar Nushi was found dead on the streets of Baghdad with multiple stab wounds and other signs of torture.
Explosion was followed by a car bombing in the Iraqi capital that killed at least nine people.
24 are thought wounded in the midnight attack.
The Mercer's 19th annual Quality of Living survey takes into account a city's infrastructure, transport connections, economic instability, social unrest and growing political upheaval which affect the quality of living.
Islamic State sleeper cells in east Mosul mark the start of a new insurgency.
At least 48 have been killed in a car bomb blast near car dealerships.
Thousands were in Baghdad's Tahrir Square after cleric Moqtada al-Sadr called for a protest.
Iraqi soldiers in eastern Mosul have celebrated victory by pausing for selfies with Daesh corpses.
As Iraqi forces push Isis out of Mosul, IBTimesUK looks at the impact on southern Iraq
Attack comes two days after dozens were killed in twin suicide bombings in Shia areas of Baghdad.
54 others have also been injured in the attack at a busy market in central Al Sinak neighbourhood.
IBTimes UK presents its top reports from journalists who have been far afield in 2016.
Most of those who supported Islamic State in northern Iraq have fled or been arrested.
Acting Iraqi Interior Minister Aqeel al-Khazali expects suicide attacks in major Iraqi cities
IBTimes UK Special Report: The fighters ride to battle under wooden crucifixes and Shia paramilitary flags
The troops are about 3km away as they advance under heavy fire.
As the assault on the city has begun, convoys of Iraqi, Kurdish and US forces moved east of Mosul.
The lunchtime attack in the Shaab neighbourhood wounded at least 60 more.
Isis has claimed the blast in Baghdad al-Jadida in an online statement.
At least 34 others injured in attack.
The Islamic State claimed the attack through its propaganda outlet Amaq.
Rockets which launched from the weapons cache hit eight separate locations in Baghdad.
Iraqi officials have repeatedly warned Thamer al-Sabhan not to intervene in domestic matters.