Meanwhile, a powerful typhoon hit Japan's southern islands, injuring 21 people, and the Meteorological Agency warned the storm could bring heavy rains and mudslides to areas hit by the temblors.
The two offshore quakes Sunday - the first with a magnitude of 6.9 followed by a 7.3-magnitude temblor five hours later - were felt most strongly in sparsely populated areas in southwestern Wakayama state, about 280 miles west of Tokyo.
They also shook the major cities of Osaka, Kyoto and Nagoya, and caused buildings to sway in Tokyo.
The National Police Agency said 38 people were hurt, including three people with broken bones. Most were injured in the second, more powerful quake.
Aftershocks continued to rattle the region early Monday, including a magnitude-5.7 tremor, according to the Meteorological Agency. No damage or injuries were immediately reported.
"A series of magnitude-5 aftershocks could continue up to the next 10 days. They could cause tsunami waves, and I urge people to evacuate to higher ground," public broadcaster NHK quoted Yoshinobu Tsuji, assistant professor at the University of Tokyo's Earthquake Research Institute, as saying Monday.
Tsunami - waves triggered by seismic activity - as high as 3 feet were recorded along the Pacific Coast Sunday, though the Meteorological Agency lifted its tsunami warnings early Monday.
Kyodo News agency also reported that 600 homes were without electricity, while high-speed train services were temporarily suspended.
Also Monday, Typhoon Songda was packing winds of up to 90 miles per hour as it headed across the East China Sea toward Japan's southernmost main island of Kyushu, the Meteorological Agency said.
Police said 21 people had been injured by the storm and tens of thousands of homes were without electricity, NHK said.
Though the typhoon is still far away from quake-hit areas, the Meteorological Agency said the storm could bring heavy rains and warned that landslides were increasingly likely following the temblors.
The two quakes late Sunday occurred far off Japan's Pacific coast, which may have minimized damage.
The first quake was centered about 70 miles off the coast of Wakayama on the Kii peninsula and the second was centered about 80 miles off the coast of Kochi state.
Japan, which rests atop several tectonic plates, is among the world's most earthquake-prone countries.
A magnitude 7 quake is capable of causing widespread, heavy damage.
In 1995, a magnitude-7.2 quake in the western port city of Kobe killed 6,400 people.