Kazakhstan and Belarus also surrendered nuclear weapons they inherited after the collapse of the Soviet Union.
Ukraine has four nuclear power stations and German magazine Bild quoted a Ukrainian official specialising in weapons procurement who said that Kyiv could build a nuclear missile.
“We have the material, we have the knowledge. If the order is given, we will only need a few weeks to have the first bomb,” he said. “The West should think less about Russia’s red lines and more about our red lines.”
Sources in Ukraine agreed that although there was an element of posturing and brinkmanship in the Ukrainian statements, they should still be taken seriously.
Nato has promised Ukraine membership of the Western military alliance but has not set a date, frustrating Mr Zelensky who said “an immediate invitation to Ukraine to join Nato would be decisive” in the war against Russia.
One security source in Ukraine told The Telegraph that Mr Zelensky and his government were getting desperate.
“There is an understanding that countries with nukes are treated differently,” the source said. “This is an existential conflict for Ukraine, something people in the West still don’t seem to get.”
Many analysts, though, said that even if Ukraine had a nuclear missile, it was unlikely to act as a deterrent.
Instead, Pavel Podvig, a senior researcher at the United Nations Institute for Disarmament Studies, said that a nuclear-armed Ukraine would just increase the danger of nuclear war.
“How would a nuclear Ukraine deter nuclear Russia?” he asked. “How would nuclear weapons have helped Ukraine in Crimea? In eastern Ukraine? It’s not the magic wand people seem to think it is.”
Ankit Panda, of the Carnegie Endowment for International Peace, a Washington-based think tank, said Mr Zelensky talking about nuclear weapons would not be a “winning strategy” in “bargaining with Nato going forward”.