The most respected voice for Iraq’s Shiite majority on Friday joined calls for the country’s prime minister to form an inclusive government or step aside, a day after President Barack Obama challenged Nouri al-Maliki to create a leadership representative of all Iraqis.

Grand Ayatollah Ali al-Sistani’s thinly veiled reproach was the most influential to place blame on the Shiite prime minister for the nation’s spiralling crisis.

The focus on the need to replace al-Maliki comes as Iraq faces its worst crisis since the withdrawal of U.S. troops in 2011. Over the past two weeks, Iraq has lost a big chunk of the north to the al-Qaeda-inspired Sunni militants of the Islamic State of Iraq and the Levant, whose lightning offensive led to the capture of Mosul, the nation’s second-largest city.

The gravity of the crisis has forced the usually reclusive al-Sistani, who normally stays above the political fray, to wade into politics, and his comments, delivered through a representative, could ultimately seal Mr. al-Maliki’s fate.

Calling for a dialogue between the political coalitions that won seats in the April 30 parliamentary election, al-Sistani said it was imperative that they form “an effective government that enjoys broad national support, avoids past mistakes and opens new horizons toward a better future for all Iraqis.”

Deeply revered by Iraq’s majority Shiites, al-Sistani’s critical words could force Mr. al-Maliki, who emerged from relative obscurity in 2006 to lead the country, to step down.