There are two groups promoting the concept that Islam is tolerant of terrorism. The first is those wishing to hijack Islam for their political purposes and have distorted and misquoted religious text to justify their abhorrent actions. The second are those who wish to spread fear and hatred of Muslims to suit their political or economic agendas, and similarly distort and misquote religious text to claim that Islam condones such abhorrent actions.
However, mainstream traditional Muslims are and always have been very vocal in condemning both such extremist groups.
There is no room for terrorism in Islam. One does not need a religious text to know such acts are reprehensible; nonetheless, the Islamic tradition is clear that there is no room for terrorism. The prophet Muhammad (peace be upon him) expressly forbade aggression and the killing of women and children and unarmed men in combat. Maulana Abdul Shakoor writes in his book, "A Brief Account of the Prophet's Life":
"Physical Jihad is permissible only for the persecuted and as a defense against tyranny. In other words, Jihad is another name for defense of independence. To look upon the battles of the time of the Holy Prophet (peace be upon him) as not conditioned by self-defense and self-preservation is not only un-Islamic but also ignorance." (More)