BAGHDAD — Iraqi Prime Minister Nouri al-Maliki’s days at the helm of his country appear to be numbered after his own party seemed resigned to finding another candidate for the post, releasing a statement urging politicians not to “cling” to their positions.

Shiite politicians were meeting Sunday night to discuss other names for the premiership, lawmakers said. A day earlier, Maliki’s Dawa party said it in its statement that politicians should “adhere to the principle of sacrifice” for the sake of the country.

Maliki’s coalition won the largest share of the vote in elections in April, but not a majority, making him reliant on political alliances to form a government. But with many blaming him for the turmoil that has convulsed the country since the polls, Some parties are digging in their heels to prevent him from ruling for a third four-year term.

But even more problematic for Maliki have been hints from Grand Ayatollah Ali Sistani that it is time for him to step aside. The reclusive Shiite cleric might be the most influential figure in Iraq, with his words closely followed by millions across the country. Although he normally avoids directly embroiling himself in politics, his sermons have become increasingly pointed.

The Dawa party’s statement Saturday echoed a sermon delivered on behalf of Sistani on Friday, which also urged politicians not to hold on to their positions and to expedite the formation of a new government.

On Saturday, Sheik Abdul Halim al-Zuhairi, a senior figure in Dawa, was dispatched to Najaf to deliver a message to Sistani that the coalition was willing to replace Maliki if necessary, said Jumaa al-Atwani, a politician with Maliki’s coalition. Zuhairi passed the letter to Sistani’s son, he said. But Hayder al-Khoei, an associate fellow at London-based Chatham House, said associates of Sistani had denied that the visit took place. Regardless, he said, the odds appeared stacked against the embattled Iraqi leader.

“It’s clear now that both Dawa and Sistani know that Maliki can’t stay for a third term,” Khoei said. “The key question is: Will he go quietly?”