The Greek prime minister, Alexis Tsipras, has been invited to Berlin during a new low in Greco-German relations, after the Greek finance minister, Yanis Varoufakis, was forced to deny "giving the finger" to Germany in a two-year-old YouTube video.

The German leader, Angela Merkel, invited Tsipras for his first visit to Berlin since he came to power in January on an anti-austerity platform that has led to clashes with Greece's creditors, including Germany.

This is soon after Varoufakis, appearing via videolink on Günther Jauch, one of Germany's most-watched political discussion programmes on the state TV channel ARD, was shown a video of himself criticising the Greek government for accepting the European Union's bailout conditions.

In the video, filmed at a conference in Zagreb in May 2013, the finance minister said in English: "Greece should simply announce that it is defaulting, just like Argentina did, within the euro in January 2010, and stick the finger to Germany" – at which point he appeared to raise his middle finger – "and say, 'Well, you can now solve this problem by yourself'."