The two leaders met for talks in Linkoping in southern Sweden and visited Saab, which is the maker of the JAS 39 Gripen fighter, the GlobalEye surveillance aircraft, missile systems, anti-tank infantry weapons and other equipment.
Kristersson told a news conference the two countries had signed a long-term co-operation agreement over air defences.
The co-operation included the possibility of exporting 100-150 new Gripen E fighter jets in what would easily be Sweden's biggest ever aircraft export order.
"We fully realise it's a long road ahead of us," Kristersson said with a Gripen in Swedish livery in the background.
"But from today we are committed to exploring all the possibilities in providing Ukraine with a large amount of Gripen fighters in the future."
The possibility of supplying Gripens to Ukraine has been under consideration over the past two years but was put on hold to allow Ukraine to focus on the introduction of US-made F-16 fighters that it began deploying last August.
"We have started the work to obtain Gripens to Ukraine and expect the future contract to allow us to acquire no less than 100 such jets," Zelenskiy said, speaking through a translator.
Ukrainian pilots have been in Sweden to test the Gripen and help smooth any eventual export of the jets, a rugged and relatively low-cost option compared to aircraft such as the US F-35.
Zelenskiy said Ukraine aimed to receive and start using Swedish Gripen jets next year.
"For our army, Gripens are a priority. It is about money, about manoeuvres," he told the press conference.
Kristersson said that nothing was decided yet but estimated that production and delivery of the first new aircraft could take three years.
The Gripen has been in commission since 1996 and Saab has produced about 280 of the planes in total.
Sweden has ordered 60 of the latest Gripen E model and Saab is increasing capacity in Linkoping, aiming to be able to produce 20-30 planes per year at the plant in a couple of years.
Saab is also building Gripens in Brazil.
Before arriving in Linkoping, Zelenskiy briefly touched down in Oslo where the Norwegian government announced it was donating another 1.5 billion Norwegian crowns ($A229.7 million) to Ukraine for the purchase of natural gas to secure electricity and heating.
Russian authorities said on Wednesday they had carried out a major training exercise involving nuclear weapons, a day after the United States announced a delay in plans for a second summit between presidents Vladimir Putin and Donald Trump on the Ukraine war.
The Kremlin released video showing General Valery Gerasimov, head of the General Staff, reporting to Putin on the drills.
Russia said it fired missiles from ground launchers, submarines and aircraft, including intercontinental ballistic weapons that are capable of striking the United States.
At key moments in the war in Ukraine, Putin has issued reminders of Russia's nuclear might as a warning signal to Ukraine and its allies.
The NATO military alliance has also been conducting nuclear deterrence exercises this month.
