The exchange on Saturday came hours after Kyiv came under a large-scale Russian drone and missile attack that left at least 15 people injured.
Ukrainian President Volodymyr Zelenskiy and Russia's defence ministry said each side brought home 307 more soldiers on Saturday, a day after each released a total of 390 combatants and civilians.
"We expect more to come tomorrow," Zelenskyy said on his official Telegram channel.
Russia's defence ministry also said it expected the exchange to be continued, though it did not give details.
Hours earlier, explosions and anti-aircraft fire were heard throughout Kyiv as many sought shelter in subway stations as Russian drones and missiles targeted the Ukrainian capital overnight.
In talks held in Istanbul in May - the first time the two sides met face to face for peace talks since Russia's 2022 full-scale invasion - Kyiv and Moscow agreed to swap 1000 prisoners of war and civilian detainees each.
Officials said Russia attacked Ukraine with 14 ballistic missiles and 250 Shahed drones overnight while Ukrainian forces shot down six missiles and neutralised 245 drones - 128 drones were shot down and 117 were thwarted using electronic warfare.
Kyiv officials said the swap, on the border with Belarus, was one of the biggest combined missile and drone attacks on the capital.
"A difficult night for all of us," the city administration said in a statement.
Posting on X, Ukraine's Foreign Minister Andrii Sybiha called it "clear evidence that increased sanctions pressure on Moscow is necessary to accelerate the peace process".
Separately, 13 civilians were killed on Friday and into Saturday in Russian attacks in Ukraine's south, east and north, regional authorities said.
Three people died after a Russian ballistic missile targeted port infrastructure in Odesa on the Black Sea, local Governor Oleh Kiper said.
Russia's defence ministry claimed its forces overnight struck various military targets across Ukraine, including missile and drone-producing plants, a reconnaissance centre and a launching site for anti-aircraft missiles.
The prisoner swap on Friday was the first phase of a complicated deal involving the exchange of 1000 prisoners from each side.
Zelenskiy said the first phase of the deal brought home 390 Ukrainians, with further releases at the weekend making it the largest swap of the war.
Russia's defence ministry said it received the same number of people from Ukraine.
However, the exchange - the latest of dozens of swaps since the war began and the biggest involving Ukrainian civilians so far - did not herald a halt in the fighting.
Battles continued along the roughly 1000km front line and neither country has relented in its deep strikes.
After the May 16 Istanbul meeting, Turkish Foreign Minister Hakan Fidan called the prisoner swap a "confidence-building measure" and said the parties had agreed in principle to meet again.
But Kremlin spokesman Dmitry Peskov said on Friday that there has been no agreement yet on the venue for the next round of talks as diplomatic manoeuvring continued.
Russian Foreign Minister Sergey Lavrov said Moscow would give Ukraine conditions for a "sustainable, long-term, comprehensive" peace agreement, once the ongoing prisoner exchange had finished.
European leaders accuse Russian President Vladimir Putin of dragging his feet in peace efforts while he tries to capture more Ukrainian land.
The Istanbul meeting revealed that both sides remain far apart on key conditions for ending the fighting.
One such condition for Ukraine is a temporary ceasefire as a first step toward a peaceful settlement.
with PA
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