The deadly attack on Wednesday came as US Secretary of State Antony Blinken visited Kyiv and was expected to announce more than US$1 billion ($1.57 billion) in new American funding.
Associated Press journalists at the site of the attack in Kostiantynivka saw covered bodies on the ground and emergency workers extinguishing fires at market stalls, with blackened and mangled cars nearby.
Prime Minister Denys Shmyhal said at least 16 people were killed. At least 28 were wounded, according to Internal Minister Ihor Klymenko.
Emergency service workers extinguished the fire that damaged about 30 pavilions at the outdoor market, Klymenko said. Crews searched the rubble for any trapped civilians.
Twenty shops, power lines, administrative building and the floor of an apartment building were damaged, according to the prosecutor general's office.
Blinken's visit also was aimed at assessing Ukraine's three-month-old counteroffensive and signal continued US backing as some Western allies express worries about Kyiv's slow progress in driving out Russian forces after 18 months of war, according to US officials.
"We want to make sure that Ukraine has what it needs, not only to succeed in the counteroffensive but has what it needs for the long-term, to make sure that it has a strong deterrent," Blinken said.
"We're also determined to continue to work with our partners as they build and rebuild a strong economy, strong democracy."
Blinken was set to pledge more than US$1 billion in new US funding, a senior State Department official said, speaking on condition of anonymity in order to discuss the announcement before it was made.
The money would be for "a range" of investments, the official said, without elaborating.
Other issues, including support for Ukraine's war-torn economy were to be discussed, building on Blinken's June announcement in London of US$1.3 billion ($2 billion) in aid to help Kyiv rebuild, with a focus on modernising its energy network, which was bombarded by Russia last winter.
Kremlin spokesman Dmitry Peskov said that US assistance to Ukraine "can't influence the course of the special military operation" — Moscow's euphemism for the war.
Blinken arrived in Kyiv for an overnight visit hours after Russia launched a missile attack on the city. He was expected to meet with President Volodymyr Zelenskyy and other top officials to discuss the ongoing counteroffensive and reconstruction efforts.
On the train journey to Kyiv, Blinken met with Danish Prime Minister Mette Frederiksen, also on an official visit, to discuss the war. Blinken thanked her for Denmark's leadership in a coalition training Ukrainian pilots on F-16s and for promising to donate the fighter jets to Ukraine, according to State Department spokesperson Matthew Miller.
Washington officials said there will be discussions of alternative export routes for Ukrainian grain following Russia's exit from the Black Sea Grain Initiative and its frequent bombardment of port facilities in the Odesa region, from which most grain is transported abroad.
Those alternatives may include new overland routes, or ships hugging coastlines to keep out of international waters where they could be targeted by Russia's navy.
After arriving in Kyiv, Blinken laid a wreath at the city's Berkovetske cemetery to commemorate members of the Ukrainian armed forces who lost their lives defending the country.
Blinken told Foreign Minister Dmytro Kuleba that the US has "seen good progress in the counteroffensive. It's very heartening."
Meeting with Shmyhal, Blinken said he was in Ukraine "to reaffirm our commitment to stand with you … to help ensure that you succeed militarily in dealing with the aggression, but also to stand with you to make sure that your efforts to build a strong economy and a strong democracy succeed."
Shmyhal said Ukraine is grateful the money is coming in the form of grants, not loans that would drive it into debt.
Overnight, Russia fired cruise missiles at Kyiv in its first aerial attack on the capital since August 30, according to Serhii Popko, the head of Kyiv's regional military administration.
Debris from a downed missile struck a business in Kyiv, causing a fire and damage. No casualties were reported.
In the Odesa region, one person was killed in a Russian missile and drone attack on the port of Izmail that damaged grain elevators, administrative buildings and agricultural enterprises, authorities said.
The trip was Blinken's fourth visit to Ukraine since the war began, including one very brief excursion over the Polish-Ukrainian border in March 2022, just a month after the Russian invasion. But it will be the first time America's top diplomat spends the night in the capital since he visited Kyiv in January 2022, before the invasion.