The US attack on Wednesday came after a wave of strikes on Iran-linked targets in Iraq and Syria last week following the killing of three American troops in neighbouring Jordan on January 28.
The US Central Command (CENTCOM) said the commander killed Wednesday was targeted "in response to the attacks on US service members".
The strike killed "a Kataeb Hezbollah commander responsible for directly planning and participating in attacks on US forces in the region," according to CENTCOM.
Iraqi authorities slammed the strike as a "blatant assassination" in a residential neighbourhood of Baghdad.
"The international coalition is completely overstepping the reasons and objectives for which it is present on our territory," said Yehia Rasool, the military spokesman for Iraq's prime minister.
He was referring to the US-led military coalition formed in 2014 to fight the Islamic State group -- the year the jihadist group overran nearly a third of Iraq's territory.
Rasool later announced in a statement that talks with Washington on the "end of the mission" would resume on Sunday.
A first round of talks opened on January 27 following a request by Iraqi Prime Minister Mohamed Shia al-Sudani for a timetable for the withdrawal of US-led troops.
It was swiftly suspended after the deadly drone strike in Jordan the following day.
Kataeb Hezbollah -- which announced it was suspending its operations against US forces after the Jordan attack -- said one of its commanders had been killed, identifying him as Abu Baqr al-Saadi.
The commander, whose funeral was held on Thursday, was responsible for "military affairs" in Syria, an official from the group told AFP.
An interior ministry official said a total of three people -- two Kataeb Hezbollah leaders and their driver -- had died in the strike, which was carried out by a drone in the east Baghdad neighbourhood of Mashtal.
- 'Red lines' -
The latest US strike sparked condemnation in Iraq, with a pro-Iran parliamentary bloc dubbing it an attack on "Iraqi sovereignty".
Washington has "crossed all red lines by targeting regular forces and men who contributed to defeating Islamic State terrorism," said the Coordination Framework, an alliance of pro-Iran Shiite parties.
Iraq's pro-Iran Al-Nujaba movement promised a "targeted retaliation", saying that "these crimes will not go unpunished".
Iran joined in the condemnation on Thursday, with foreign ministry spokesman Nasser Kanani calling the strike an act of "adventurism" that was "a threat to regional and international peace and stability".
US and allied troops have been targeted more than 165 times in the Middle East since mid-October in attacks linked to the Israel-Hamas war in Gaza.
The majority of the attacks have been claimed by the Islamic Resistance in Iraq, a loose alliance of Iran-backed groups angered by US support for Israel.
Iraq analyst Sajad Jiyad, of the New York-based Century Foundation think tank, said he expected the tensions to continue to spiral.
"These groups have a lot of capabilities, they are active in several countries now, the US is willing to engage, to retaliate, to kill members of these groups," he said.
"The US is giving no indication it is going to pull back or stand down its military activity in the Middle East," he said, adding "it is very difficult to suddenly see an end to the tensions."
Washington has some 900 troops in Syria and 2,500 in Iraq as part of the coalition against IS.
Its troops in Iraq are deployed at the invitation of Baghdad, but those in Syria are located in areas outside Syrian government control.
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