The wreck of a car - presumed to be the bomber's - lay near the attack site
The president of the Russian republic of Chechnya, Ramzan Kadyrov, says Moscow has ordered him to help fight insurgents in neighbouring Ingushetia.
The president of Ingushetia, Yunus-Bek Yevkurov, was wounded in an apparent assassination attempt on Monday.
Speaking to the Reuters news agency, Mr Kadyrov said the Russian leadership had told him to intensify operations in both Chechnya and Ingushetia.
Both republics have experienced an upsurge in violence over recent months.
President Yevkurov is still fighting for his life in hospital.
Human rights abuses
Mr Kadyrov, whose own father Akhmad was killed by a bomb in 2004, has brought relative calm to Chechnya, but human rights groups accuse his militias of widespread abuses.
He has often been accused by critics for being responsible for ordering the murder in 2006 of Russian investigative journalist Anna Politkovskaya, something he has repeatedly denied.
On Tuesday Mr Kadyrov said he had been ordered by Russia's Dmitry Medvedev to run operations in both countries.
He told Reuters: "He told me to intensify actions... including in Ingushetia. I will personally control the operations... and I am sure in the near future there will be good results."
In October Mr Yevkurov replaced Murat Zyazikov, who was criticised for boosting the rebellion with his heavy-handed tactics.