ISTANBUL – Two weeks into the demonstrations that have shaken Turkey, Prime Minister Recep Tayyip Erdogan’s formerly rock-solid support has begun to soften.

Some loyal political Islamists, including an influential civil society movement, have criticized his on-again, off-again crackdown. And in the Istanbul neighborhood that is his political home, many said Friday that they still supported him but were uneasy with the methods used against the protesters.

Erdogan remains by far the most popular politician in Turkey, and supporters say pro-government rallies this weekend will give his voters a chance to show their strength. But divisions have opened among his base, with especially harsh criticism coming from a movement led by Islamic scholar Fethullah Gulen, a once-staunch Erdogan backer who has questioned the government’s handling of the crisis from self-imposed exile in Pennsylvania.

With riot police using tear gas and water cannons on protesters in Taksim Square twice in the past two weeks, many here fault Erdogan’s decisions for escalating a crisis that began as a small, peaceful protest against plans to replace Gezi Park, the last green space in central Istanbul, with a replica of an Ottoman-era barracks that once stood on the site.

After an initial police crackdown May 31, demonstrations quickly spread to dozens of cities across the country, and complaints broadened to include more fundamental personal freedoms.

In a 41/2-hour closed-door meeting with opposition representatives Friday, Erdogan offered a plan to wind down the protests. He said he would wait for a court to rule whether his plans for Gezi Park were legal. Even if he won the court case, he would put the decision to a citywide referendum, he said in a speech.

Many in Taksim Square and adjoining Gezi Park were skeptical that the concessions were enough to get the protesters to return home. And across Turkey, splits among Erdogan supporters suggested that a new political calculus had begun to emerge. His party won a sweeping parliamentary mandate in 2011, built on a faithful core of conservative Muslims who had long felt disenfranchised.

In trying to prevent one wrong, “50-fold more wrongs are being committed, sparking more rancor and hatred,” Gulen said last week, according to the Gulen-affiliated Today’s Zaman newspaper. Of the protests, he said, “don’t disregard them.”

The Gulen Movement’s support was vital to Erdogan’s initial successes, analysts say, and although there has been tension between Erdogan and Gulen for several years, it has rarely been so open. The Gulen Movement is a civil society group that promotes education and religious tolerance but carries an air of secrecy and mystery akin to the Masons. Despite his absence, Gulen’s sermons and proclamations carry outsize weight in Turkey, where many believe his loyalists have a substantial presence in the police force and judiciary.

“No one should underestimate the Gulen sect,” said Mehmet Baransu, a journalist at the Taraf newspaper.