To the east and west lie the Russian republics of North Ossetia and Karachayevo-Cherkessia.
One of his aides said he was recovering from a back injury in North Ossetia.
Hostages have been seized in Vladikavkaz, in North Ossetia to the west, and in Makhachkala in Dagestan to the east.
Incumbents have recently lost in Krasnoyarsk in Siberia, Penza in Russia's heartland, Karelia on the Finnish border and North Ossetia in the Caucasus.
Mr Mutsolgov says the war in Georgia found little support in Ingushetia, not long ago engaged in a bitter ethnic conflict with North Ossetia.
Mr Basayev Russia's most wanted man was also behind the attack in September 2004 on a school in Beslan, in the neighbouring region of North Ossetia.
An ethnic cauldron of more than 20 nationalities, Dagestan is becoming steadily more violent, while a land dispute between North Ossetia and next-door Ingushetia has flared again.
Women were also part of the gang that took over a school in Beslan, North Ossetia, in 2004 - an attack which ended in 334 deaths, including 186 children.
In mid-September, the Kolka Glacier in the Caucasus Mountains collapsed, submerging villages in the Republic of North Ossetia (Russian Federation) under thousands of tons of ice and rock, killing over 120 people.
Mr Zyazikov had come in for sustained criticism from opposition groups over his perceived failure to combat corruption, solve disputes with North Ossetia over refugees or reduce attacks on the security forces by Islamists.
Mukharbek Aushev, who is head of the north Caucasian faction in Russia's parliament and certainly no fanatic alleges that powerful forces in Moscow want to set Chechnya, Dagestan, his native Ingushetia and possibly North Ossetia (Russia's best friend in the region) at loggerheads.
He has spoken of the people of North and South Ossetia as an "integral whole" and issued a joint statement with his South Ossetian counterpart on boosting links.
Indeed, Russia's recognition of South Ossetia and Abkhazia could easily reignite separatist sentiment in the north Caucasus.
Mr Medvedev's recognition of Abkhazia and South Ossetia may also have unpredictable consequences for Russia's north Caucasus.
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