"We've been working for 19 or 20 hours without sleep and without rest," said Larysa Borysenko, one of the rescuers, whose team had found bodies but no survivors.
Ukraine's national police service gave the new toll in a statement while the head of Dnipropetrovsk region, Valentyn Reznichenko said two children were among the dead.
The "fate of another 35 residents of the building is unknown," he said, confirming that rescue operations were ongoing, some 40 hours after the strike.
Emergency service workers with rescue dogs dug for survivors into the night Sunday in the wake of one of the deadliest recent attacks of Russia's nearly year-long invasion.
The Kremlin told reporters Monday its forces were not responsible for the attack and pointed to an unsubstantiated theory circulating on social media that Ukrainian air defense systems had caused the damage.
"The Russian armed forces do not strike residential buildings or social infrastructure. They strike military targets," Kremlin spokesman Dmitry Peskov said.
Ukraine leader Volodymyr Zelenskyy said late Sunday that search operations would go on as long as necessary and condemned Russian's "cowardly silence" over the attack.
The EU's most senior diplomat, Josep Borrell, late Sunday described the strike as "inhumane aggression" and vowed "there will be no impunity for these crimes."
"The EU will continue supporting Ukraine, for as long as it takes," he added.
The rising cost of the strike that ripped open the side of a housing block came as Russia and its close ally Belarus announced the beginning of new joint military drills.
Belarus, which has been a key ally to Russia throughout the conflict, allowed Moscow's forces to use its territory as a launching pad for its assault last February.
Its defense ministry said in a statement the air force exercises would involve joint "tactical" flights and that every airfield in Belarus would be involved.
"The exercise is purely defensive in nature," Pavel Muraveyko, first deputy state secretary of Belarus's Security Council, said in remarks carried Sunday by the defence ministry.
Since Ukrainian forces pushed back Russian troops from the north of the country, Kyiv and its Western allies have been assessing the threat of another assault from Belarusian territory.
The Institute for the Study of War, based in the United States, said in an analytical note Monday that the risk of a new offensive from Belarus was "low" and "the risk of Belarusian direct involvement was very low".
Ukraine in recent weeks has been pressing Western backers to supply its forces with advanced tanks, in particular the German-designed Leopard model.
The UK this weekend pledged 14 Challenger 2 tanks to Ukraine, which would make it the first Western country to supply the heavy tanks Kyiv has been calling for.
Peskov, the Kremlin's spokesperson, told reporters Monday that fighting in Ukraine would continue with or without the deliveries.
"These tanks are burning and will burn," he said.
NATO Secretary General Jens Stoltenberg said in an interview with German media on Sunday that "recent pledges for heavy warfare equipment are important -- and I expect more in the near future".
Separately on Monday, Ukraine officials said that Russian forces had continued shelling the southern city of Kherson, which was recaptured by Kyiv's forces late last year.
The regional governor Yaroslav Yanushevych said one woman was killed in an attack on a residential building and that Russian forces also damaged an empty children's hospital.
In Crimea, the Ukrainian Black Sea peninsula annexed by Russia in 2014, the Moscow-appointed official responsible for the military city Sevastopol said Russian forces had downed seven drones over the last 24 hours.