As of Tuesday afternoon, more than 50 people were still listed as unaccounted for, the newspaper said.
The most extreme rainfall and flooding concentrated in southwestern Japan in the Okayama prefecture and around Hiroshima.
The death toll reached at least 114, NHK public television said, with 61 people missing.
But he has now come in under fire, after photos posted on Twitter showed him at a party with lawmakers just as rains intensified.
Abe has seen his support rates rebound after slumping over a suspected cronyism scandal and is keen to prevent any declines ahead of a ruling-party leadership race in September.
An official in Okayama prefecture told AFP news agency that water levels were gradually receding and that emergency teams may be able to access the worst-hit areas on foot.
He says the United Nations chief "commended the government's efforts to help people affected and expressed his admiration for the domestic search and rescue teams helping those in need". Survivors recounted narrow escapes.
It's the worst weather-related disaster in the country since 2011, when almost 100 people were killed by two typhoons in August and September. "We are fully committed to life-saving rescue and evacuation", he said.
The city of Kurashiki, with a population of almost 500,000, has been hit hardest by the torrential rain that pounded western Japan with three times the usual amount for July. "We did not realize it was becoming such a big deal".
(Reuters/Issei Kato) A woman stands in a flooded area in Mabi. Some two billion yen (S$24 million) of reserve funds has been set aside.
"When necessary amounts firm up. we would consider an extra budget later on if these funds prove insufficient". Officials in Ehime prefecture asked the central government to review a weather warning system, noting that rain warnings were issued after damage and casualties were occurring.
The rising waters have forced 2 million people from their homes and thousands of houses are damaged while thousands more are still without power. According to the city, there are around 4,600 flooded houses, while evacuees from the entire district are estimated to be between 3,000 and 5,000. In some areas, hills collapsed under the weight of water, causing deadly landslides that crushed homes and took out roads. "Finding a place to live in, even if it's temporary, is our top priority". The death toll is higher than that seen in 2014, when more than 70 people died in landslides caused by torrential rain in Hiroshima.
Heavy rains hit much of western Japan from Thursday last week, with 583 millimetres of rain falling between Friday and Saturday morning alone.
Though the weather has cleared up, the disaster goes on. "Rivers overflowed, turning towns into lakes, leaving dozens of people stranded on rooftops".
It's also one of the deadliest natural disasters to hit the island nation since an quake struck off the coast of Tohoku in 2011, triggering a massive tsunami that crippled the Fukushima Daiichi Nuclear Power Plant.