BERN, June 15 (Reuters) - Ukrainian President Volodymyr Zelenskiy on Thursday urged Switzerland to allow the re-export of weapons to Ukraine, saying the move would be vital in defeating Russia's invasion.

Neutral Switzerland has a long-standing policy of barring any country that buys its arms from re-exporting them to parties in a conflict. In November last year it imposed an embargo on Swiss munitions being sent to either Russia or Ukraine.

"I know there is a discussion in Switzerland about the exportation of war materiel to protect and defend Ukraine. That would be vital," Zelenskiy said in a video address to both houses of the Swiss parliament. "We need weapons so we can restore peace in Ukraine."

The issue has sparked extensive debate in Switzerland, which has had to balance its foreign policy tradition of neutrality while considering the concerns of its European neighbours and its domestic weapons industry.

Zelenskiy, wearing a plain black T-shirt with the word "Ukraine" printed across his chest, thanked Switzerland for adopting EU sanctions over the invasion but said more was needed.

"It is very important to show solidarity because these sanctions will help us to end aggression," he said. "We have to strengthen the sanctions."

Despite having adopted EU sanctions and frozen Russian assets worth 7.5 billion Swiss francs ($556 million), Switzerland has denied requests from Germany, Denmark and Spain to re-export Swiss ammunition, weaponry and military vehicles to Ukraine.

Germany has also asked Swiss authorities to sell mothballed Leopard 2 tanks to arms maker Rheinmetall, which would allow the company to backfill gaps in the armaments of European Union and NATO members that have sent tanks to Ukraine.

In his speech, Zelenskiy invited Switzerland to host a global peace summit on Ukraine. He said he had spoken to Swiss President Alain Berset about the initiative in March.

A spokesperson for the Federal Department of Home Affairs said the Swiss president had had several exchanges with Zelenskiy this year but declined to comment on a possible summit.

Zelenskiy's address was preceded by days of cyber attacks against Swiss government websites claimed by a pro-Russian hacking group.

It also triggered tensions in parliament, with the right-wing Swiss People's Party (SVP) snubbing the speech and saying it was in violation of the country's neutrality.