MOSCOW — Under the attentive eye of Russian state television, several hundred pro-Russian demonstrators in the city of Donetsk, in eastern Ukraine, declared on Monday that they were forming an independent republic and urged President Vladimir V. Putin to send troops to the region as a peacekeeping force, even though there was no imminent threat to peace.

The actions in Donetsk and two other main cities in eastern Ukraine, which included demands for a referendum on seceding from Ukraine and joining Russia, seemed an effort by the activists to mimic some of the events that preceded Russia’s invasion and annexation of Crimea. However, there were no immediate indications that the Kremlin was receptive to the pleas.

While widely regarded as political theater supported if not directed by the Kremlin, the protests could help promote what analysts say is Russia’s primary goal of destabilizing the shaky government in Kiev, preventing it from drifting further into the West’s orbit and giving Moscow leverage over the country’s future ahead of presidential elections in May.

The turmoil in eastern Ukraine also makes it extremely difficult for the provisional government in Kiev to begin putting in place an array of austerity measures and financial overhauls required by the International Monetary Fund as a condition for an $18 billion loan package that the country desperately needs to avert a financial default.