“I am sure Putin wants to destroy our alliance, not by attacking it but by splintering it,” he said in a speech to military and political leaders in Berlin, as quoted by The Telegraph.
He warned that Mr Putin could try to destabilise a NATO member by using a rebel militia as in eastern Ukraine, or other forms of “ambiguous” warfare.
In the absence of an overt Russian attack, some NATO members could be reluctant to invoke Article 5 of the Washington treaty, under which an attack on one member is an attack on all.
“Once Article 5 is gone, our alliance is over,” Gen Hodges said.
He called for American tanks to be positioned in countries along NATO’s eastern flank, as a deterrent to Mr Putin.
Just months after moving its last tanks out of Europe, the US has decided to send some 220 Abrams tanks and Bradley fighting vehicles back in response to the Ukraine crisis.
Gen Hodges said he had proposed positioning some of the tanks in Poland, Lithuania, Latvia, Estonia, Romania and Bulgaria.
And the US has already agreed to send troops to Poland and the three Baltic states.
Gen Hodges called for NATO countries to maintain defence spending in the face of the Ukraine crisis.
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