Photographs showed Kneissl, 53, smiling in a long white and cream "dirndl" dress and talking to Putin as they danced in a vineyard in southern Styria province, the venue of her wedding to entrepreneur Wolfgang Meilinger.
The SPD is a coalition partner with German Chancellor Angela Merkel's conservative bloc. Putin and Merkel hold three-hour talks and are mostly on the same page.
On Friday, Merkel said that Germany is looking into the possibility of such a summit: "A meeting between Germany, France, Turkey and Russian Federation could make sense - this must be well-prepared, so there is no date yet".
On Iran, the Russian president said he would discuss with Merkel the Iran nuclear deal between world powers and Iran.
Ukraine fears the pipeline will allow Russia to cut it off from the gas transit business, while Germany's eastern European neighbors, nervous of Russian encroachment, have also raised concerns about the project.
Putin also spoke about global reconstruction efforts and the humanitarian situation in Syria. Merkel has said a certain level of gas transit through Ukraine must be ensured.
"We need to strengthen the humanitarian effort in the Syrian conflict", he said on Saturday before the evening meeting with the German chancellor at...
The worldwide coverage of Putin's visit would bring priceless publicity, he added.
The two leaders planned to make statements before the talks.
Yet the foreign ministry insisted that Putin's visit "will not change anything in terms of Austria's foreign policy positions".
Earlier this month, a Russian suggestion that the United States and Russia form a joint group to finance infrastructure renovation in Syria was met with an icy reception, according to a U.S. memo seen by Reuters. But she was appointed to her job by the far-right Freedom Party (FPO) which has a cooperation agreement with Putin's United Russia party.
In his comments, Peskov said Merkel and Putin had a "general exchange of opinions" over the situation in Ukraine and that the leaders expressed regret that implementation of the so-called Minsk accords had stalled.
However Putin's attendance was originally described as a "private event" by Kneissl's office but has since been upgraded to a "working visit".