KUWAIT CITY — The United States’ attempts to isolate Iran, including by punishing Iraqi militias and politicians who are supported by Iranian officials, has deepened tensions not only between Washington and Baghdad but also within the Trump administration.

American military and intelligence officials said the increasing pressure on Iraq risks infuriating its Parliament, including politicians linked to Iran, which could limit the movements of the 5,200 United States troops based in Iraq.

Secretary of State Mike Pompeo, whose confrontational stand on Iran has already strained ties with European allies, is leading the push for Iraq to confront its fellow Shiite-majority neighbor. He arrived in the Middle East on Tuesday to speak with officials in Kuwait, Israel and Lebanon about containing Iran.

Under plans recommended by Mr. Pompeo and some White House officials, the State Department would designate Iran’s military Islamic Revolutionary Guards Corps as a foreign terrorist organization. It would be a first instance of the United States designating a unit of another government’s military as a terrorist group. American officials said it could put United States troops and intelligence officers at risk of similar actions by foreign governments.