MOSCOW — Viktor F. Yanukovych of Ukraine and the Ukrainian opposition leaders signed an agreement on Friday that ended the deadly protests in Kiev by promising a new constitution and early elections. But the Russian president’s envoy to Kiev refused to co-sign it. While Moscow welcomed an end to the violence, it basically viewed the agreement as a diktat by the Western-backed Ukrainian opposition. The opposition has seized power in Kiev, and Moscow is wary that the crisis will not end anytime soon. Some radical groups remain well-armed; there are deep political, cultural and regional cleavages in Ukrainian society; the country’s elites are in disarray; and its economic situation is rapidly deteriorating. The mess is very much Ukraine’s own, and Russia has far less influence on it than is commonly appreciated.

The most popular myth about Moscow’s role in the Ukrainian crisis is that Mr. Yanukovych has been but a puppet of President Vladimir V. Putin. In reality, Mr. Putin has been very frustrated with his Ukrainian counterpart. To Mr. Putin, Mr. Yanukovych is unreliable, forever vacillating between the European Union and Russia; and now, a totally spent force, he has fled from Kiev to Kharkiv, a Russian-speaking city in eastern Ukraine. Moscow knows that the Ukrainian oligarchs, most of whom used to support Mr. Yanukovych, are largely anti-Russian. Though they in effect rule Ukraine, they fear being taken over by the richer business giants next door. Even those who made their money in Russia, like the protest-funder Petro Poroshenko, prefer to keep it in the West.

The protests erupted when Mr. Yanukovych refused to sign the so-called association agreement between Ukraine and the European Union, which would have established a free-trade area, among other things. Despite what he claims, it wasn’t the Kremlin that made him do that. Moscow had clearly signaled it did not want Kiev to sign the deal when it introduced de facto sanctions on Ukrainian products last year, but ultimately Mr. Yanukovych was guided by his own calculations, rather than Putin’s admonitions or advice. The fundamental reason Mr. Yanukovych demurred was fear that he would not be re-elected in 2015 if he signed the agreement. At some point he realized that the deal would bring no financial support from the European Union and saw no way to offset the inevitable drop in trade with Russia or cushion the blow to Ukraine’s Soviet-era heavy industry.

During the months of standoffs in Kiev, Russia’s actual role was much more modest than advertised by the international media or the rumor mill in Kiev. The Russian ambassador to Ukraine, Mikhail Zurabov, was conspicuously absent from public view. The Kremlin ordered all Duma members to stay out of Ukraine. Dmitry Rogozin, a deputy prime minister and a former Russian ambassador to NATO with a knack for making in-your-face comments about the West, has largely remained silent on Ukraine. The only Russian official to display any continuous interest in Ukraine was Sergey Glazyev, Putin’s adviser for Eurasian integration, who spoke at conferences and wrote articles about the high costs of Ukraine’s turn to the European Union.