(Adds U.S. State Department comment)
BAGHDAD, May 19 (Reuters) - A rocket was fired into the Iraqi capital Baghdad's heavily-fortified Green Zone, which houses government buildings and foreign embassies, on Sunday but caused no casualties, the Iraqi military said.
"A Katyusha rocket fell in the middle of the Green Zone without causing any losses," the military said in a statement, adding it landed near the Monument of the Unknown Soldier.
The monument lies in open ground about half a kilometre (a third of a mile) north of the sprawling, riverside U.S. embassy compound. The blast was heard across central Baghdad, according to Reuters witnesses and residents.
A U.S. State Department official confirmed a "low-grade" rocket landed in the Green Zone near the embassy, but said there were no casualties or significant damage.
The embassy in Baghdad and U.S. consulate in the Iraqi Kurdish regional capital Erbil evacuated non-emergency staff this week, out of apparent concern about perceived threats from Iraq's neighbour, Iran.
The U.S. State Department official noted that there had so far been no claim of responsibility, and that no U.S.-inhabited facility was impacted.
"But, we take this incident very seriously," the State Department official said. "We will hold Iran responsible if any such attacks are conducted by its proxy militia forces or elements of such forces, and will respond to Iran accordingly."
President Donald Trump's administration has said it sent additional forces to the region to counter what it called credible threats from Iran against U.S. interests, including from militias it supports in Iraq.
Tehran has described U.S. moves as "psychological warfare" and a "political game."
Both Iran and the United States have said they do not want war.
Hours after the blast in Baghdad, Trump wrote on Twitter: "If Iran wants to fight, that will be the official end of Iran. Never threaten the United States again!"
The Katyusha multiple rocket launcher is an inexpensive type of rocket artillery that can deliver explosives to a target quicker than conventional artillery, but is less accurate.
After the blast, Iraqi police special forces found a rocket launcher in eastern Baghdad's al-Sina district, about 7 km (4.3 miles) away across the Tigris River from the Green Zone, and sealed off the area, a police source told Reuters.
Officers were searching for suspects and an ordinance disposal team from the Baghdad Operations Command was inspecting the launcher, the source said.
The Green Zone was regularly targeted by mortars during the U.S. occupation of Iraq that ended in 2011.
Rockets have occasionally been fired into the Green Zone since then. The latest such incident was in September, when three mortar shells landed inside the Green Zone, causing no casualties. (Reporting by John Davison, Ahmed Rasheed and Ahmed Aboulenein in Baghdad, and Raya Jalabi in Erbil; Additional reporting by David Lawder and Phil Stewart in Washington; Writing by Ahmed Aboulenein and Raya Jalabi; Editing by Mark Potter, Emelia Sithole-Matarise and Daniel Wallis)