Answer by taking a quote from the following article:

Alexander Valterovich Litvinenko (Russian: Aleksandr Val'terovich Litvinenko, IPA: [aljI'ksandr 'valtir@vjItc ljItvjI'njenk@]; 30 August 1962 (Or 4 December 1962 by father's account - 23 November 2006) was a British naturalised Russian defector and former officer of the Russian FSB secret service who specialised in tackling organised crime. According to US diplomats, Litvinenko coined the phrase Mafia state. In November 1998, Litvinenko and several other FSB officers publicly accused their superiors of ordering the assassination of the Russian tycoon and oligarch Boris Berezovsky.

Litvinenko stated that "all the bloodiest terrorists of the world" were connected to FSB-KGB, including Carlos "The Jackal" Ramirez, Yassir Arafat, Saddam Hussein, Abdullah Ocalan, Wadie Haddad of the Popular Front for the Liberation of Palestine, George Hawi who led the Communist Party of Lebanon, Ezekias Papaioannou from Cyprus, Sean Garland from Ireland, and many others. He said that all of them were trained, funded, and provided with weapons, explosives and counterfeit documents to carry out terrorist attacks worldwide and that each act of terrorism made by these people was carried out according to the task and under the rigid control of the KGB of the USSR. Litvinenko said that "the center of global terrorism is not in Iraq, Iran, Afghanistan or the Chechen Republic. The terrorism infection creeps away worldwide from the cabinets of the Lubyanka Square and the Kremlin".  When asked in an interview who he thought the originator of the 2005 bombings in London was, Litvinenko responded saying, "You know, I have spoken about it earlier and I shall say now, that I know only one organization, which has made terrorism the main tool of solving of political problems. It is the Russian special services."  Litvinenko also commented on a new law that "Russia has the right to carry out preemptive strikes on militant bases abroad" and explained that these "preemptive strikes may involve anything except nuclear weapons." Litvinenko said, "You know who they mean when they say 'terrorist bases abroad'? They mean us, Zakayev and Boris and me." He also said that "It was considered in our service that poison is an easier weapon than a pistol." He referred to a secret laboratory in Moscow that still continues development of deadly poisons, according to him.

Did Litvinenko support terrorism?
He said that all of them were trained, funded, and provided with weapons, explosives and counterfeit documents to carry out terrorist attacks worldwide