The visit, which marks the 50th anniversary of the start of Soviet gas deliveries to Austria, takes him to one of Europe's more Russia-friendly countries at a time when relations between the European Union and Russian Federation are at a low ebb.
Russian President Vladimir Putin said on Thursday there were no plans to shut down social media sites or limit internet freedoms in Russia, and that a "civilized" solution was needed to make the internet safer.
Almost two months ago, authorities began blocking the Russia-developed Telegram app over its refusal to share encryption data with intelligence agencies.
After Tuesday's talks, the managers of Russia's state-controlled gas giant Gazprom and Austria's OMV signed an agreement on Russian natural gas supplies through 2040, a deal Putin said highlights the two nations' "significant contribution to energy security in Europe".More news: Multistate salmonella outbreak linked to pre-cut melon
The poisoning of former Russian double agent Sergei Skripal and his daughter in Britain further strained the EU-Russia ties.
Putin, who has ruled Russian Federation since 2000, was re-elected for his fourth term in office in March and, barring changes to the Constitution, will not be able to run again in 2024. He suggested the stadiums could add cafes and shopping malls to boost their profitability. "They see that Russian Federation has become a competitor to them ... we propose that this is a very mistaken policy".
Asked about the poisoning during his annual call-in show on Thursday, Putin said he does not want to comment on the cause of their illness and said Russian Federation is still seeking consular access to both of them and to their case files.
Speaking in an interview with the Austrian ORF television broadcaster late Monday, Putin said he wouldn't comment on allegations that a referendum could keep him in power after his current term ends.More news: Philly Doesn’t Care What Trump Says About the Eagles
Mr Putin also said the government will be looking to streamline the tax system in order to fight poverty, but denied speculation that Russian Federation was considering abandoning its flat-rate income tax.
Austrian exports to Russia declined sharply after European Union sanctions in 2014 were met by Russian sanctions.
On Thursday he said Russia's gross domestic product is now 1.5% higher than a year ago. He described it as modest but said he is confident that future "growth is guaranteed".
Putin will meet liberal President Alexander Van der Bellen as well as Kurz, a 31-year-old conservative who became chancellor in December at the head of a coalition with the far-right Freedom Party. Putin travels to Austria in a first European Union trip since his re-election.More news: How to watch Golden Knights vs. Capitals