Thousands of people in the Urals city of Yekaterinburg protested this week against Orthodox Church plans to recreate a pre-Soviet cathedral in a popular central park.
"Today, we have suspended work," Alexandre Vyssokinski said, according to the TASS news agency.
The authorities will canvass local opinion so as to determine the project's future, he added.
Earlier Thursday, Putin said that "if people are against it, that opinion must be respected."
He also suggested -- as promised by Vyssokinski -- that there should be "a survey, and the minority should concede to the majority."
Putin's comments were unusual in that over almost two decades in power, the president has brooked little dissent, overseeing crackdowns on public protest and the opposition.
"Steps need to be taken from both sides to resolve this issue from the point of view of people who live there," he said.
Dozens of people have been arrested over the clashes at the construction site in Yekaterinburg, some 1,000 miles (1,700 kilometres) east of Moscow.
Local authorities have backed the project, and the oligarch head of one of Russia's largest copper producers has also offered financial support.
"Usually, people ask for a cathedral to be built," Putin said.
"Cathedrals should unite, not divide people," he added.
The row has exposed tensions over the growing authority of the Orthodox Church in Russia.
Presidential spokesman Dmitry Peskov had earlier decried "provocations" and "false information" in relation to the cathedral, praising the actions of law enforcement in the dispute.