The offensive launched on August 6 caught the Kremlin off guard, with Kyiv claiming to have captured dozens of settlements and more than 1,200 square kilometres (nearly 500 square miles) of territory.
"Ukraine has a right to defend itself. And according to international law, this right does not stop at the border," Stoltenberg said in an interview with Die Welt published Saturday.
"The Russian soldiers, tanks and bases there (Kursk) are legitimate targets under international law."
The offensive also surprised Kyiv's allies, with Stoltenberg saying Ukraine "did not preview its planning" with NATO and that the Western military alliance "played no role".
Stoltenberg also welcomed Germany's commitment to remain Ukraine's largest European military donor and second-largest worldwide, as Berlin prepares cuts to its aid to Kyiv in next year's budget.
Chancellor Olaf Scholz's government came under fierce criticism for the decision last week. He says Germany will continue to supply the outgunned and outmanned Ukrainian military with the equipment it needs.
The Kursk offensive has changed little on the front line in eastern Ukraine, where Russia continues to claim incremental gains, including three villages on Friday.
Ukrainian President Volodymyr Zelensky has acknowledged his army faces an "extremely difficult" situation near the strategic hub of Pokrovsk, in the Donetsk region, with Russian troops closing in.
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