With a greatest hits album due for later in March, a concert tour is scheduled across Europe starting from April and stretching into November.
The band were due to perform in St Petersburg on June 29, before going to a gig in Moscow on July 1.
However, the band tweeted: “We are cancelling our Russian shows that are scheduled for this summer. The only reason for this is the invasion of Ukraine by the Russian state.”
They made clear: “We love Russia. This great country has inspired our band through its art and literature, and since we first played there seventeen years ago, we have built a rich and deep relationship with our Russian fans.
“Since Thursday morning, we have spoken to many of our friends in Russia via social media and have encountered unanimous opposition to this violence and solidarity with our Ukrainian friends.
“We know you see the madness of your country’s leadership. We know you do not want war.
“We do not want war. Despite the tragedy of this situation, we still burn a flame of optimism in our hearts and look forward to the day when we can return in a time of peace to share the joy of music together again.”