Kay-Achim Schönbach said the idea that Russia wanted to invade Ukraine was nonsense. He added that all President Vladimir Putin wanted was respect.
A number of countries have supplied weapons to Ukraine, including the US and UK. But Germany has refused Ukraine’s request for ammunition.
Russia has denied claims that it is planning to invade Ukraine.
But President Putin has issued demands to the West which he says concern Russia’s security, including that Ukraine be stopped from joining the military defence alliance Nato.
He also wants Nato to abandon military exercises and stop sending weapons to eastern Europe, seeing this as a direct threat to Russia’s security.
Mr Schönbach said on Saturday that he had resigned from his role “with immediate effect” in order to “avert further damage”.
He made the controversial comments while speaking at a think-tank discussion in India on Friday and the video was later published to social media.
“It is easy to give him the respect he really demands – and also probably deserves,” he said.
He added that the Crimean peninsula, which Russia annexed in 2014, “is gone and will never come back”.
The head of Nato has warned there is a real risk of a fresh conflict in Europe after an estimated 100,000 Russian troops amassed on the border.
Some 90 tonnes of US “lethal aid” arrived in Ukraine on Saturday, and the UK announced earlier this week that it was sending defence weapons and extra troops for training. Several other Nato members are sending military equipment or deploying forces.
Germany has refused to send weapons, instead offering to send Ukraine a field hospital. It has reportedly blocked attempts by Estonia to send Ukraine German-origin weapons, according to the Wall Street Journal.
Defence Minister Christine Lambrecht told Welt am Sonntag newspaper that Berlin had already delivered respirators to Ukraine and severely injured Ukrainian soldiers are being treated in German military hospitals.
Ukraine has denounced Germany’s response, accusing Berlin of undermining Western unity by refusing to transfer weapons to Ukraine or allowing some of its allies to do so.
In an interview with Sky News on Sunday, Ukraine’s ambassador to the UK, Vadym Prystaiko, called on Germany to play a “significant role”.
“If they’re not ready to provide us with weapons, defensive weapons, OK, they might do something else which will help us,” he said.
Mr Prystaiko said he would “absolutely” like to see Germany block Russia’s Nord Stream 2 gas pipeline.
The pipeline runs from Russia to Germany under the Baltic Sea, and, if granted regulatory clearance, would increase Moscow’s gas exports to Europe. The Ukrainian presidency has described it as a “dangerous geopolitical weapon”.
Approval for the project is currently being decided by Germany’s energy regulator.