Austrian Chancellor Karl Nehammer is the first European leader to hold face-to-face talks with Russian President Vladimir Putin since Moscow invaded Ukraine.
Nehammer travelled to the Russian capital on Monday and said that he aimed to act as a "bridge-builder" between Moscow and Kyiv.
He said he is hoping to "do everything possible to make (the war) stop" and to "ensure that steps are taken in the direction of peace".
"We are militarily neutral, but there are exceptions to neutrality. We are not neutral when it comes to naming crimes and discussing them," he said at a joint press conference with Ukrainian President Volodymyr Zelenskyy in Kyiv on Saturday.
Austria is not a member of NATO, having declared itself permanently neutral in 1955. The Alpine country has not sent weapons to Ukraine, instead providing humanitarian aid and body armour and helmets for civilians.
Nehammer, a conservative, previously said that he has been moved by his conversations with Zelenskyy and stated he wants to show support.
While in Ukraine, Nehammer also toured the town of Bucha, the site of alleged war crimes carried out by Russian troops -- something that many expect him to discuss with Putin.
"It is necessary that the UN investigates these violations, that international justice begins its work," he said in Kyiv. "It is well known that the wheels of international prosecution turn slowly, but they turn continuously and with persistence, and that is what is happening at the moment."
After the announcement of Nehammer's visit to the Kremlin, criticism of his plans appeared in some German-language media and from at least one Ukrainian official.
Sergei Orlov, deputy mayor of the besieged Ukrainian city of Mariupol, told Germany's outlet Bild that such a trip was unacceptable at the moment.
"The war crimes that Russia is committing right now on Ukrainian soil are still taking place," Orlov said during a TV broadcast.
"I don't understand how a conversation can be held with Putin at this time, how business can be conducted with him."