Two weeks after Ukraine’s surprise incursion into Russia, the Kremlin’s forces have slowed the advance, with the hardening front line in the Kursk region of Russia setting up the next phase of a battle with great political stakes for both sides.

President Vladimir V. Putin of Russia has pledged a decisive response to the first invasion of Russian territory since World War II. But so far, the response has been focused on containing the incursion rather than reversing it, raising the question of what Russia’s depleted military is willing to risk to expel the invaders — or if it is capable of doing so.

The unforeseen invasion of Kursk has exposed the ongoing intelligence failures of the Russian military as well as Moscow’s shortage of battle-ready reserves in a war fought along a 750-mile front. Ukraine’s rapid gains have also upended the global perception of a slow but unstoppable Russian march toward victory in a war of attrition.

As Ukrainian forces advanced, videos of surrendering groups of Russian conscripts and border guards shocked many in Russia, shaking Mr. Putin’s narrative that the war in Ukraine was being fought far away by well-paid, determined volunteers.

Still, the battle in Russia’s border regions remains in its initial stages, and the present pace of the Kursk incursion is giving Mr. Putin time to calibrate his response. Instead of weakening the Kremlin’s grip on power, the invasion may eventually cause more Russian citizens to rally around the flag, analysts said.

The Kursk invasion “is certainly a blow to the Kremlin’s reputation,” Tatiana Stanovaya, a Russian political scientist, wrote on social media on Tuesday. But “it is unlikely to spark a significant rise in social or political discontent among the population, nor will it lead to an elite rebellion.”