Interior Ministry spokesman Murat Zurabov told RFE/RL from Nazran that the explosions occurred as Prime Minister Ibragim Malsagov's motorcade passed by.
"Two powerful explosions went off," Zurabov said. "As a result, two members [of Malsagov's] escort were wounded. The head of the government was also wounded. One of the Interior Ministry officers who was accompanying [Malsagov] died of his wounds in hospital."
In comments made to Russian news agencies, Ingushetia's acting Interior Minister Beslan Khamkhoev said the explosions were caused by remote-controlled roadside bombs. He described the attack as an assassination attempt against the prime minister. But Zurabov told RFE/RL that it is not yet certain the attack was meant to kill Malsagov.
Khamkhoev said the bombs were placed about 15 meters apart and detonated within 10 seconds of each other.
Malsagov sustained head and leg injuries and was unconscious when he arrived at the hospital. But Zurabov said Malsagov's life was not in danger.
There has been no immediate claim of responsibility for the attacks.
Russia's RTR television reported that Ingushetian President Murat Zyazikov and Russian President Vladimir Putin's representative in the Southern Federal District, Dmitrii Kozak, held emergency consultations over the phone.
Ingushetia has witnessed increasing violence in recent months, mostly against police officers and government officials. Some of these attacks are believed to be connected with the war in neighboring Chechnya.
Zyazikov survived a suicide car-bomb attack near Nazran in April 2004. Two months later, militants reportedly linked to radical Chechen field commander Shamil Basaev raided Nazran by night, killing several top security officials.
Khamkhoev said he believes those attacks and today's bombings are the work of "forces that do not like the positive developments that are taking place in Ingushetia." He did not elaborate.
The 44-year-old Malsagov was appointed prime minister on 30 June. He had previously supervised the construction of Ingushetia's new capital, Magas, before taking over the republic's Construction Ministry in January 2003.