Political and security sensitivities for leaders in both countries led the U.S. move cautiously to secretly set up the so-called fusion intelligence center in Baghdad. But Mr. Obama’s announcement Thursday that the U.S. will deploy up to 300 military advisers and set up two joint operations centers shows the extent to which U.S. and Iraqi leaders are racing to catch up to an ISIS threat they had already identified but were slow to counter.

As Prime Minister Nouri al-Maliki, a Shiite, struggles with the Sunni insurgency and the sectarian divisions that spawned it, support for his own leadership came under fire on Friday by the country’s most influential Shiite cleric. Mr. Maliki, who is trying to assemble a governing coalition following April elections, should consider stepping aside, a spokesman for Grand Ayatollah Ali al-Sistani said during a Friday sermon.

To battle ISIS, U.S. and Iraqi leaders are taking steps proposed but not taken over the past months and years, including setting up larger intelligence operations and deploying teams of special operations forces. The small team set up last year “wasn’t a priority and nobody thought it was a serious effort,” said a senior U.S. official.