Mr Yevkurov was appointed President in the hope he would bring stability
The two men who organised the attempted assassination of the president of Ingushetia have been killed by security forces, Russian officials say.
The head of the Federal Security Service, Alexander Bortnikov, said the two men were linked to the Muslim insurgent group, Ingush Jamaat.
The FSB said the two men - named only as Dzortov and Aliyev - were killed in what it called as a "combat operation".
President Yunus-Bek Yevkurov was badly injured in the attack in June.
"The crime against Ingush President Yunus-Bek Yevkurov, committed in June this year, has been solved," Mr Bortnikov told a session of the Russian Anti-terrorism Committee in Moscow.
"Its organisers - heads of the Ingush Jamaat, Dzortov and Aliyev - have been killed as a result of an operational combat action."
"The investigation surrounding the attacks is ongoing," the FSB chief added.
The attack on Mr Yevkurov was one of a number against high-profile targets in Russia's northern Caucasus region this year, where an insurgency is spreading.
Although Russian forces have largely suppressed the insurgency in Chechnya, violence has spilled over into neighbouring Ingushetia and Dagestan.
Mr Yevkurov suffered head and internal injuries in the attack on his car in June, and has taken several months to recover. However, he has resumed his presidential duties and last week sacked his cabinet for failing to tackle poverty and corruption.