A powerful 7.2-magnitude earthquake rocked the U.S.-Mexico border region Sunday, causing power outages in both countries as it sent out seismic waves felt from Los Angeles to Arizona and Tijuana.

The quake happened at 3:40 p.m. PT in the Mexican state of Baja California, about 60 kilometres southeast of Mexicali, the state's capital city, according to the U.S. Geological Survey. The area has been hit by 3.0-magnitude quakes all week.

More than 900,000 people live in the greater Mexicali area.

It was the largest earthquake in the region in nearly 18 years and was followed by aftershocks or distant "triggered" earthquakes on both sides of the border, U.S. Geological Survey seismologist Lucy Jones said.

A multi-storey parking structure collapsed at Mexicali's city hall but no one was injured, said Alfredo Escobedo, the state's civil protection director.

The tremor's epicentre was 10 kilometres below ground, Mexico's National Seismological Service reported.

Hundreds of people in Tijuana fled the border city's beaches fearing a tsunami, said Capt. Juan Manuel Hernandez of the Tijuana fire department.

Tsunami experts quickly reported that no tsunami was expected along the West Coast, and Hernandez said the beach filled back up with people within an hour.

Tijuana Fire Chief Rafael Carillo said firefighters were rescuing people trapped in an elevator at the Ticuan Hotel in downtown Tijuana, but were mostly responding to reports of fallen cables and minor damage to buildings.

Power and phone service were out in Mexicali, and Mexico's Federal Electricity Commission said it was evaluating the damage. The tremor also forced the closure of gas stations in northern Baja and ruptured a segment of highway.

In Los Angeles, the city fire department went on "earthquake status," and some stalled elevators were reported. No damage was reported in Los Angeles or San Diego.

More than 5,000 people across southern California experienced brief electricity outages, mostly with about 30 seconds of flickering lights.

Several hundred dealt with longer outages.

Strongest in 18 years

In Arizona, more than 3,000 customers in the Yuma area had a "relatively momentary outage" from the quake, Arizona Public Service Company spokesperson Don Wool said.

The 7.2-magnitude quake was felt as far north as Santa Barbara, Calif., seismologist Susan Potter said. It was one of the strongest to hit the state in recent history. Only one has been stronger - a 7.3-magnitude quake that hit Landers, about 70 kilometres north of Palm Springs, and left three dead in 1992.

Seismologists also said smaller quakes were triggered in a geothermal area in northern California.

A quake with a preliminary magnitude of 4.0 was recorded at 3:49 p.m. PT about 40 kilometres north of Santa Rosa.

A dispatcher with the Sonoma County Sheriff's Department said the agency had not received any emergency calls after the quake.