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."
"Steps need to be taken from both sides to resolve this issue from the point of view of people who live there," he said.
He also suggested -- as promised by Vyssokinski -- that there should be "a survey, and the minority should concede to the majority."
Social media images showed the mayor speaking in front of a crowd of several hundred booing protestors.
Putin's comments followed the latest clashes Wednesday which saw some 70 arrests made.
They were unusual in that over almost two decades in power, the president has brooked little dissent, overseeing crackdowns on public protest and the opposition.
At the same time, Putin has appeared to back an increased role for the Orthodox Church in Russian, helping focus nationalist feeling, and the planned cathedral was seen as part of this policy.
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.
"It is very likely that there were some people in Yekaterinburg who provoked the protestors... and that quite naturally drew the appropriate response from the security forces," Peskov said.
The cathedral, first mooted nine years ago, is meant to replace one destroyed by the Soviet authorities in 1930. Completed by 2023, it would tower some 66 metres (205 feet) above the park in a a city well known for its liberal traditions.
Yekaterinburg was home to Russian president Boris Yeltsin and until recently it was run by a mayor widely regarded as one of the few remaining public voices critical of Putin.
The outcry against the project appears to reflect tensions generated by gains for conservative groups and the Orthodox church in recent years at the expense of more liberal trends in Russia.