He called on “saner minds” to challenge the decision, which saw a previous city council ruling prohibiting the march reversed.
The event has been planned to mark 69 years since Nazi troops ousted the Soviet red Army and entered the Latvian capital. The invasion led to the capture and murder of some 75000 Jews.
The decision to allow the march to proceed comes just days before an official Holoacust memorial visit by Israeli Foreign Minister Avigdor Liberman to visit.
The Prime Minister Valdis Dombrovskis said he was "puzzled and upset" the march would not be banned.
Mr Dombrovskis said: "The Latvian government respects human rights guaranteed by the constitution and the court's independence, but freedom of expression cannot extend to Nazi propaganda.”
Every March a parade is held in the country for veterans of the Latvian Legion of the SS, which was founded on Adolf Hitler's orders in 1943.
The Conservative Party in Britain came under fire this year for being aligned in Europe with the group who organise it.
