LOS ANGELES — The Ringling Brothers and Barnum & Bailey Circus train has been bringing four-ton Asian elephants to this city since 1919.

But “The Greatest Show on Earth” might have made its last stop here.

Los Angeles is poised to ban elephants from performing in circuses within its city limits, after pressure from animal welfare advocates who have for decades condemned the methods used to train and transport elephants as abusive and cruel.

If the City Council adopts the ban early next year, Ringling Brothers, the oldest continuously operated circus in the country, will be barred from the nation’s second-largest city unless its owners agree to abandon one of the show’s signature acts.

“The treatment of elephants in traveling circuses is one of the crueler practices, and it’s time for us to stand up for them,” said Paul Koretz, the City Council member who sponsored the ban. He predicted that once Los Angeles outlawed circus elephants, other communities would follow. “At some point, this will be universally banned throughout the country,” he said.