But the church, represented by the ACLU of Utah, said it contends the ordinance is unconstitutional and will continue its effort to have a federal judge strike the city law.
"We are thrilled that our clients are no longer being banned from public sidewalks merely because they would like to express their views, assemble and freely exercise their religion," said John Mejia, ACLU of Utah legal director, in a statement.
The church wanted to hand out "biblically-based" literature about temples and Christian beliefs during the open house at the temple, which ends Saturday.
Attorney Richard Van Wagoner, representing the city, said the officials agreed to temporarily not enforce the ordinance to avoid costly litigation and after the church agreed to limit participation to four protesters on each sidewalk.
"The city maintains that its Free Speech Ordinance meets all constitutional protections while advancing its compelling interest in public safety," Van Wagoner said in a statement.
Brigham City's ordinance is similar to one adopted by other Utah cities, he noted, adding that Salt Lake City's ordinance was upheld as constitutional by a federal court judge.
City Manager Bruce Leonard said Thursday that the ordinance, adopted in 2010, was aimed at protecting pedestrian and vehicle safety during large-scale events.