The newspaper reported that the request sparked deep concern among Pentagon and State Department officials.
Officials said the Pentagon did develop options for striking at Iran, but it was not clear if the White House, or President Trump himself, received or knew about the request, or if a serious strategy was being considered.
U.S. President Donald Trump's National Security Adviser John Bolton asked the Pentagon last fall to draw up plans to strike Iran, rattling the Defense and State Departments, according to a report published Sunday.
According to the paper, Mira Ricardel, the former deputy national security adviser, described the attacks in Iraq as "an act of war", and said that the U.S. needed to respond accordingly. "People were shocked. It was mind-boggling how cavalier they were about hitting Iran", former USA high-ranking official told The WSJ.
But they triggered unusual alarm in Washington, where Mr. Trump's national security team led by John Bolton conducted a series of meetings to discuss a forceful American response, including what many saw as the unusual request for options to strike Iran.
Most Americans blame Trump, Republicans for partial gov't shutdown
Some Trump allies have been encouraging him to declare a national emergency and redirect other funds to begin building the wall. That ended when congressional Republicans agreed to a short-term funding bill for closed agencies that was later extended.
The militant assault on the diplomatic quarter by a Shiite group aligned with Iran landed in an empty lot with no casualties reported.
The US blamed Iran for the attack, despite Tehran's categorical denial.
A spokesman for the National Security Council was quoted in the Wall Street Journal, however, as saying: "We continue to review the status of our personnel following attempted attacks on our embassy in Baghdad and our Basra consulate, and we will consider a full range of options to preserve their safety and our interests".
Asked about the report during his Middle East trip, US Secretary of State Mike Pompeo declined to comment.
On Sunday, Iran's foreign ministry summoned a senior Polish diplomat in protest at Poland jointly hosting a global summit with the U.S. focused on the Middle East, particularly Iran, state news agency IRNA reported. "If they're responsible for the arming and training of these militias, we're going to go to the source".