BUENOS AIRES, Argentina — After facing a wide backlash, the International Olympic Committee on Sunday restored wrestling — one of the most traditional and elemental sports — to the Summer Games.

Chastened by calls to modernize its leadership and energize its matches, wrestling changed its rules, created more weight classes for women and easily prevailed over squash and a combined bid by baseball and softball.

Wrestling received 49 votes, compared with 24 for baseball/softball and 22 for squash in voting by delegates of the Olympic committee. The vote, which was to add one of the three sports, guaranteed that freestyle and Greco-Roman wrestling would be contested at least through the 2020 Summer Games in Tokyo and the 2024 Olympics, which have yet to be awarded.

Last February, in what was seen as a wake-up call, the 15-member executive board of the IOC removed wrestling from the core sports of the Summer Games after the 2016 Rio Olympics. The move drew heavy criticism because wrestling has been an integral Olympic sport.

But Olympic officials complained to wrestling officials that their sport had antiquated leadership and matches that could be dull, with results not easily understood by spectators.

Wrestling’s world governing body, known by its initials as FILA, quickly began to reform itself. Its president, Raphael Martinetti of Switzerland, resigned and was replaced by a burly and gregarious Serb named Nenad Lalovic.

“We have made mistakes,” Lalovic said. “We admitted it. We have decided to listen and learn.”

A seven-month push was made to repair the standing of wrestling, which made its first appearance in the ancient Olympic Games in 708 B.C. and has been a staple of the modern games.

Countries with profound political differences — the United States, Russia and Iran — found common ground when their interests converged over wrestling.

“I think everybody should watch wrestling, to see how we can manage that,” Lalovic said.

Two Olympic weight classes were dropped for men and two were added for women to enhance gender equity. Beginning with the 2016 Rio Games, there will be six classes for men and women in freestyle wrestling and six for men in Greco-Roman wrestling.

FILA officials said they were amenable to women participating in Greco-Roman wrestling in the future if there was sufficient interest.

The rules were also amended to make matches more dynamic, rewarding wrestlers who are more aggressive and punishing those who remain passive. Matches will consist of two three-minute rounds now instead of three two-minute rounds. Takedowns will count for two points instead of one, and matches will be decided on accumulated points.

Wrestlers will now have “more time to develop the fight,” Lalovic said. “In two minutes, that was practically impossible.”

Wrestlers also will have more control in determining the outcome of matches, said Alexander Karelin of Russia, who won three Olympic gold medals in Greco-Roman wrestling.

“Wrestlers have a big chance to decide on the mat, not another reason, not referee, not judges,” Karelin said.

The continuation of wrestling in the Olympics was “critically important” to the health of the sport at the grass roots level in the United States, said Jim Scherr, a former chief executive of the U.S. Olympic Committee.

While wrestling remains popular in high school and has added teams at lower college levels, it has struggled at the Division I level amid budget constraints as the vast majority of athletic departments operate in the red.

“Because of economic pressures,” Scherr said, a non-revenue-producing sport that loses its Olympic imprimatur was “a sport that’s potentially at risk.”

Both softball and baseball exited the Olympics after the 2008 Beijing Games. Baseball, unlike hockey, has not been willing to halt its season for the Olympics and commit the world’s best players to participate.

Softball apparently could not convince the IOC of its universal appeal. The United States, Japan and Australia won 11 of the 12 available medals in the four games in which the sport was contested.

Squash has never appeared in the Olympics.