Islamist rebels from the North Caucasus were behind a deadly bomb attack on Russia's busiest airport, the head of the mainly-Muslim province of Ingushetia said on Thursday.

Ingush leader Yunus-Bek Yevkurov, who heads an impoverished region neighbouring Chechnya, is the most senior Russian official to publicly blame insurgents from the North Caucasus for Monday's suicide attack on Moscow's Domodedovo airport.

These leaders of the North Caucasus underground are responsible, like Doku Umarov, Yevkurov told reporters in Ingushetia's capital, Magas, referring to a Chechen rebel chief who calls himself emir of the Caucasus Emirate.

Russia's leaders are struggling to contain a growing Islamist insurgency in the North Caucasus, a strip of impoverished, mainly Muslim provinces along predominantly Orthodox Christian Russia's southern border.

Local leaders say a mix of clan feuds, poverty, Islamism and heavy-handed tactics by law enforcement agencies has driven youths into the ranks of rebels who want to create a Sharia-based pan-Caucasus state separate from Russia.

At least 35 people were killed and over 100 injured in Monday's suicide bomb attack. No one has claimed responsibility.