Defence secretary Ben Wallace said Britain would send an unspecified number of M270 launchers, which can fire precision-guided rockets up to 50 miles – a longer range than any missile technology currently in use in the war.
Mr Zelensky has warned as many as 75 million tonnes of grain could still be stuck in Ukraine in the autumn if Russia's blockade continues.
In a statement issued by the Ministry of Defence (MoD), Mr Wallace said: “The UK stands with Ukraine in this fight and is taking a leading role in supplying its heroic troops with the vital weapons they need to defend their country from unprovoked invasion.
“If the international community continues its support, I believe Ukraine can win.
“As Russia’s tactics change, so must our support to Ukraine. These highly capable multiple-launch rocket systems will enable our Ukrainian friends to better protect themselves against the brutal use of long-range artillery, which [Vladimir] Putin’s forces have used indiscriminately to flatten cities.”
Ukrainian troops will be trained in the UK to use the equipment, Mr Wallace added.
The MoD said the decision to provide the launchers was closely co-ordinated with the US government, which said it will supply High Mobility Artillery Rocket Systems to Ukraine.
When the US announced it would be sending the missiles, Mr Putin vowed to hit new targets.
“If they are delivered, we will draw appropriate conclusions from this and use our weapons, which we have enough of, to strike at those objects that we have not yet hit,” he said in an interview with state TV channel Russia-1, which was filmed on Friday.
Kyiv’s residents awoke on Sunday to the first Russian strikes on the capital since April 28, while Moscow’s forces have also maintained steady pressure via artillery and air strikes in the eastern Donbas region.
The Russian naval blockade has imposed an economic stranglehold on Ukraine – one of the world’s biggest grain exporters – as well as threatening food supplies to some of the world’s poorest countries.
A Downing Street spokesperson said Mr Zelensky had briefed the Prime Minister on his recent visit to Ukraine, noting “the strength of the Ukrainian armed forces’ will to fight” as well as highlighting the areas where they needed more support.
“The leaders also discussed diplomatic negotiations and the efforts to end the damaging Russian blockade of Ukraine’s grain exports,” the spokesman said.
“They agreed to intensify work with other allies, including G7 leaders, to drive progress on ending Russia’s illegal invasion and supporting Ukraine’s economy.”
The UK meanwhile announced that a specialist legal and police team will be offered to assist the chief prosecutor investigating alleged Russian war crimes in Ukraine.
Justice secretary Dominic Raab was due to present a second package of support for the independent investigation, on top of the £1 million funding provided by the UK Government earlier this year.