A Study Evaluating the Safety and Efficacy of Rituximab in Combination With Glucocorticoids in Participants With Wegener's Granulomatosis or Microscopic Polyangitis

Inclusion Criteria: * Male or non-pregnant, non-nursing female * Diagnosed with Wegener's granulomatosis or Microscopic polyangiitis according to the definitions of the Chapel Hill Consensus Conference * Participants with either newly diagnosed or relapsing disease * Participants must have active disease as per the BVAS/WG greater than equal to (\>/=) 3 that would normally require treatment with cyclophosphamide (CYC) * Participants willing to practice medically acceptable contraception during and 1 year after the completion of rituximab therapy * Participants must have severe disease i.e. one or more of the major BVAS/WG items depicting severity or disease severe enough to require treatment with CYC. * Participants must be positive for either proteinase 3-antineutrophil cytoplasmic antibodies (PR3-ANCA) or myeloperoxidase-antineutrophil cytoplasmic antibodies (MPO-ANCA) at the screening Exclusion Criteria: * History of severe allergic or anaphylactic reactions to human, humanized, or murine monoclonal antibodies * Participants in a severely immunocompromised state * Participants with severe heart failure (New York Heart Association Class IV) or severe, uncontrolled cardiac disease * Participants having active severe infection or history of recurrent bacterial, viral, fungal, mycobacterial or other infections * Participants who had a live vaccine fewer than 4 weeks before first dose of rituximab * Any other condition which puts the participant to undue risk for rituximab therapy as per local prescribing information or Investigator's judgment * Participants with any previous treatment with rituximab * Participants with any previous treatment with alemtuzumab * Participants who have had treatment with infliximab within the previous 3 months * Participants who have had treatment with adalimumab within the previous 2 months * Participants who have had treatment with etanercept within the previous month * Participants with any other investigational medication within the previous month