Was Islam originally considered to be a Christian sect?

There is some speculation that Islam was originally considered to be a sect of Christianity by those who claimed to be Christians, rather than a separate religion (e.g., Hinduism, Jainism). Do any early sources during the formative years of Islam make such an assertion? Muslims certainly don't believe Islam to be a Christian sect, but the Christians can easily fit it into the "Christian sect" fold as they have done it with the Mormons and Jehovah's Witnesses, since if Jehovah's Witnesses and Mormons can be classified as Christians then Islam also qualifies better for the Christians to qualify it as a Christian sect. So why keep Islam out?