In a videotape received by Aljazeera on Friday, Basayev denied any connection of Chechen fighters to recent explosions that occurred in Turkey, Spain and France.
He also accused Moscow of issuing false information about the Chechen separatist movement. Basayev has not appeared on television for at least two years.
Basayev's statement was broadcast two days after a Qatari court sentenced two Russian intelligence agents to life imprisonment for killing former Chechen leader Zelimkhan Yanderbiyev and accused Moscow of supervising the operation.
'Struggle to continue'
"Our Chechen people will continue their struggle inside Russia and we are not planning any attacks outside Russia even though we have the capability to do so," he said in Russian.
"We will not even target Russian officials who committed massacres against the Chechen people if they are in foreign
countries," Basayev added.
He criticised the assassination in February of Yanderbiyev, who was living in exile in Qatar. "This incident proves who is the terrorist and who is not," Basayev said.
"I reaffirm again that we are not planning any operations in foreign countries ... unlike the Russians who assassinated our former leader in Qatar."
Basayev also thanked fellow Muslims for their help. "We are grateful to the Turkish people for what they offer in assistance and care for the children and the wounded among our refugees in Turkey," he said.
Attacking the police
Chechen independence fighters, who score successes against police and Russian troops daily, briefly ruled a de facto independent Chechnya until President Vladimir Putin sent troops into the region in 1999 for the second time since the collapse of Soviet rule.
The fighters are led by Basayev and former President Aslan Maskhadov. Chechnya's current Kremlin-backed leaders have promised to secure their capture.
"I reaffirm again that we are not planning any operations in foreign countries ... unlike the Russians who assassinated our former leader in Qatar"
Chechen separatist chief
Last month, separatists killed almost 100 people in an attack in Ingushetia, on Chechnya's western border. Many Ingush fighters took part, underscoring how the conflict was spreading.
Basayev periodically issues statements threatening targets throughout Russia and has claimed responsibility for various
attacks. Most recently, he said his fighters had carried out the assassination of Chechnya's pro-Moscow president Akhmad Kadyrov in a bomb attack in May.
'An Arab mercenary'
In Moscow, Russian media reported on Friday that one of the main organisers of last week's raids in Ingushetia had been killed in a large-scale operation in the region.
Interfax news agency identified the man as Abu Qutayba and described him as an Arab mercenary, formerly a close associate of Jordanian rebel commander Khattab - a key figure among Chechen separatists killed two years ago.
Television showed several bloodied bodies on the ground after the operation and said 16 rebels had been detained.