Local officials also issued a warning against spreading fake news online after a tweet claiming a zebra was on the loose after the quake went viral.
Prime Minister Shinzo Abe told reporters the government was "working united, with its first priority on saving people's lives".
Authorities in western Japan say the number of people treated for injuries suffered in a strong quake Monday morning now exceeds 300.
Osaka, Japan's third most populated city, is a major business hub and tourist hotspot in western Japan.
While Japan declared that the quake registered at 6.1, the U.S. Geological Survey (USGS) measured it at a 5.3 magnitude.
The quake struck an important industrial area of central Japan.
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He said: " Theresa May has gone back on her word and offered an amendment that takes the meaning out of the meaningful vote". Pro-EU Tories were quick to voice their anger. "It all changed without Dominic Grieve or anyone else being consulted".
Japan's JXTG Nippon Oil & Energy Corp has shut all its refining units at the 115,000 barrels per day Osaka refinery after the quake, with product shipments halted.
Honda Motor Co. said production in Suzuka, in nearby Mie prefecture, was halted for checks but no problems were found and operations were back to normal.
People wait for train service to resume following an quake in Osaka, Monday, June 16, 2018.
Tractor maker Kubota Corp. said it halted two plants in the area, while air conditioner maker Daikin Industries Ltd suspended operations at two plants, one of which had restarted by noon. At least three people have died.
The quake collapsed walls and damaged roofs, with the nine-year-old girl killed after she was trapped by a damaged wall at a swimming complex north of Osaka. Another man in his 80s was killed when a bookcase fell on him.
Japan lies in a particularly earthquake-prone region and accounts for around 20% of quakes worldwide of magnitude 6.0 or more.
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"It was only slight at first, then after a few seconds everything shifted from side to side and I realised I was experiencing an natural disaster. I thought it was a nightmare because I was so confused", she said.
Kilpatrick, visiting Japan for the first time from the United States, said alarms went off nearly immediately in the hotel and a loudspeaker told guests to stay away from windows. "It felt like strong sideways shaking and lasted about five seconds, and I stayed there until it stopped". Osaka officials did not give details, but the injuries reported in Kyoto and three other neighboring prefectures were all minor.
Most trains in the Osaka area were still not running by late afternoon, police said.
Footage on national broadcaster NHK showed flooding from burst underground water pipes, train passengers forced to exit along train lines, and schoolchildren gathering outside in precautionary evacuations.
Factory lines stopped and water mains burst in Japan's Osaka area, as a magnitude 6.1 natural disaster shook second-biggest metropolis. In 1995, a magnitude 6.9 natural disaster killed more than 6,000 people when it struck in neighbouring Kobe.
No irregularities were reported at Kansai Electric's Oi, Takahama and Mihama nuclear power stations in Fukui Prefecture, and at Japan Atomic Power Co.'s Tsuruga nuclear plant, also in Fukui, according to the operators.
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