The attack was "very powerful, truly massive," Serhiy Bratchuk, spokesperson for the Odesa military administration, said in a voice message on his Telegram channel on Wednesday.

"It was a hellish night," he said, adding that details on damage and casualties will come later.

The attacks on Odesa, one of Ukraine's main ports for exporting grain, followed a pledge of retaliation by Russia after a blast on a bridge linking Russia to the Crimean Peninsula on Monday that Moscow blamed on Ukraine.

Shortly after the bridge was hit on Monday, Moscow withdrew from a year-old Black Sea grain agreement that allowed for the safe exports of Ukraine's grain, a move the United Nations said risked creating hunger around the world.

"(They're) are trying to scare the whole world, especially those who want to work for the grain corridor ... Ukraine, Turkey and the United Nations," said Bratchuk.

"But I think that all normal, rational people will look and say: Odesa was not afraid, is not afraid and will not be afraid - we will work."

Most of Ukraine was under air raid alerts on and off starting soon after midnight on Wednesday, with Russia striking other places, including a drone attack on Kyiv.

"A difficult night of air attacks for all of Ukraine, especially in the south, in Odesa," Serhiy Popko, head of the Kyiv's city military administration, said on the Telegram channel.

He said Kyiv was attacked and according to preliminary information there was some damage or casualties.

There was no immediate comment from Russia on the attacks. Pro-Kremlin military bloggers said that Moscow was using a combination of missiles and drones to attack Odesa and other regions.

The RBC-Ukraine news agency reported that there was also an attack on Crimea, with explosions sounding at the Krynychky military training grounds. Moscow annexed Crimea from Ukraine in 2014. Reuters could not independently verify the reports of the attack on Crimea.

The Moscow-backed governor of Crimea said on Wednesday that a fire broke out at the military training grounds in the Kirovske district on the Crimean Peninsula.

The fire forced the closure of the nearby Tavrida Highway, Russian-installed Governor Sergei Aksyonov of Crimea said on the Telegram messaging app.

On Tuesday, Russia's Defence Ministry said it had hit military targets in two Ukrainian port cities overnight as "a mass revenge strike" in response to the attack on the Crimean Bridge.

UN WORKS ON IDEAS FOR GRAIN EXPORTS

At the United Nations on Tuesday, U.N. spokesman Stephane Dujarric said there were a "number of ideas being floated" to help get Ukrainian and Russian grain and fertilizer to global markets. Moscow's decision raised concern primarily in Africa and Asia of rising food prices and hunger.

The Black Sea deal was brokered by the U.N. and Turkey in July last year to combat a global food crisis worsened by Russia's February 2022 invasion of Ukraine and its blockade of Ukrainian ports. The two countries are among the world's top grain exporters.

For Ukraine's part, "we are fighting for global security and for our Ukrainian farmer" and working on options to keep commitments on food supply, President Volodymyr Zelenskiy said in his nightly video address on Tuesday.

Moscow spurned calls from Ukraine to allow shipping to resume without Russian participation, with the Kremlin openly saying ships entering the area without its guarantees would be in danger.

"We're talking about an area that's close to a war zone," Kremlin spokesman Dmitry Peskov said. "Without the appropriate security guarantees, certain risks arise there. So if something is formalised without Russia, these risks should be taken into account."

Russia says it could return to the grain deal, but only if its demands are met for rules to be eased for its own exports of food and fertiliser. Western countries call that an attempt to use leverage over food supplies to force a weakening in financial sanctions, which already allow Russia to sell food.