"[His] elimination … will significantly reduce international terrorist activities in Russia and in particular, the North Caucasus," said Yevkurov, who had survived an assassination attempt by a suicide bomber in 2009.
Web sites loyal to the insurgency have reported on bin Laden's death but not yet discussed what the loss means to them or their campaign.
"It is well-known that terrorists are connected like links of a chain," Yevkurov said in a statement Tuesday.
A leading al-Qaida mentor, Jordanian Sheikh Abu Muhammad al-Maqdisi, has given public statements of support for North Caucasus rebel leader Doku Umarov, and Russian officials have said several foreign insurgents belonging to the global terror group have been killed by Russian security forces in the North Caucasus over the past year.
Political analysts dismiss government claims that al-Qaida has played a major role in the North Caucasus insurgency, although they do not rule out its influence.
Bin Laden's demise will not have a significant direct effect on the North Caucasus insurgency because of established funding networks across the Middle East, said Gordon Hahn, a senior researcher at the U.S. Monterey Institute for International Studies.
"The more sources they have, the more they can keep their operation going in tough times," said Hahn, who tracks Islamist violence in Russia. "They are very talented, motivated and I wouldn't underestimate them at all."