WASHINGTON/NEW YORK, Sept 28 (Reuters) -

The United States announced on Friday it will effectively close its consulate in the Iraqi city of Basra and relocate diplomatic personnel assigned there following increasing threats from Iran and Iran-backed militia, including rocket fire.

The decision adds to mounting tension between the United States and Iran, which is the target of increasing U.S. economic sanctions.

U.S. Secretary of State Mike Pompeo, as he explained the move, renewed a warning that the United States would hold Iran directly responsible for attacks on Americans and U.S. diplomatic facilities.

It followed recent rocket attacks that Pompeo said were directed at the consulate in Basra.

"I have made clear that Iran should understand that the United States will respond promptly and appropriately to any such attacks," Pompeo said in a statement.

Pompeo did not explicitly say whether a U.S. response was imminent, however, and other U.S. officials did not disclose potential response options.

Still, Pompeo said the threats against U.S. personnel and facilities in Iraq were "increasing and specific" and added that Washington was working with Iraqi forces and U.S. allies to address them.

"We look to all international parties interested in peace and stability in Iraq and the region to reinforce our message to Iran regarding the unacceptability of their behavior," he said.