By Dan Peleschuk and Supantha Mukherjee

KYIV/STOCKHOLM (Reuters) - Ukraine has begun discussing with Sweden the possibility of receiving Gripen jets to boost its air defences, Ukrainian President Volodymyr Zelenskiy said on Saturday after meeting Swedish Prime Minister Ulf Kristersson.

Zelenskiy's visit is his first to Sweden since Russia's invasion in February 2022 and the talks about obtaining Gripen jets, which he cast as preliminary, follow approval from the United States for Denmark and the Netherlands to send F-16 fighters to Ukraine.

"Today we discussed in detail the future steps regarding the possibility of opening the subject of receiving Swedish Gripens," Zelenskiy said at a joint news briefing with Kristersson, adding that the topic would be central to his meetings with other Swedish officials.

In June, the Swedish government said it would give Ukrainian pilots the opportunity to test its Saab-made Gripen fighter jet, but it has also said that it needs all its planes to defend Swedish territory.

Zelenskiy also said on Saturday that Ukrainian pilots had already begun training on the planes.

Kristersson made no mention of Gripens in his remarks, but condemned a Russian missile attack on the Ukrainian city of Chernihiv on Saturday that killed seven people and wounded 90.

"It only reinforces the need for us to stand with your in all your struggles," Kristersson said.

Ukraine and Sweden also signed an agreement which will see Ukraine begin production of Sweden's CV90 combat vehicle.

Zelenskiy was also due to meet the speaker of Sweden's parliament the Riksdag, the supreme commander of the Swedish armed forces, and the leaders of Sweden's main political parties, according to a Swedish government statement.

Sweden has been aiding Ukraine's war efforts by supplying weapons such as tanks, anti-aircraft systems and armoured Type 90 infantry fighting vehicles.

Swedish Defence Minister Pal Jonson said on Tuesday the government was planning a new $313.5 million military support package to Ukraine, consisting mainly of ammunition and spare parts to previously delivered weapon systems.

The package will be Sweden's 13th to Ukraine since the start of the war, taking the total value of the Nordic country's aid to $1.8 billion.

(Reporting by Dan Peleschuk and Supantha Mukherjee; Additional reporting by Simon Johnson in Stockholm; Editing by Toby Chopra, David Holmes and Frances Kerry)