This is a multicenter study conducted in 3 parts. Part A is a double-blind placebo-controlled parallel-group period, and Part B and C are open-label extension periods. The primary objective of the double-blind study (Part A) is to assess the effect of Prolonged-Release Fampridine treatment on walking speed as measured by the T25FW (timed 25 foot walk) in Japanese participants with Multiple Sclerosis. The secondary objective of the double-blind portion of the study is to evaluate the safety and tolerability of prolonged-release Fampridine in this study population. The primary objective of the open-label extension study (Part B) is to evaluate the long-term safety profile of prolonged-release Fampridine. The primary objective of the additional open-label extension (Part C) is to provide participants who complete the study with continued access to prolonged-release fampridine until marketed drug can be used at the applicable site or until sponsor decision to discontinue the study.

Key Inclusion Criteria:

Part A

To be eligible to participate in Part A, candidates must meet the following eligibility criteria at screening or at the timepoint specified in the individual eligibility criterion listed (potential subjects who fail screening may be rescreened 1 time):

1. Must have a diagnosis of primary-progressive, secondary progressive, progressive relapsing, or relapsing-remitting MS as defined by the revised McDonald Committee criteria ([Lublin and Reingold 1996; McDonald 2001; Polman 2005]) of at least 2 months duration.
2. Must be able to complete the T25FW with or without a walking aid in 8 to 45 seconds at the screening visit.

Part B

To be eligible to participate in Part B, candidates must meet the following criteria at the Week 21 visit in Part A, which is the first visit for Part B:

1. Completed all visits in Part A of the study.

Part C

To be eligible to participate in Part C, candidates must meet the following criteria at the Week 52 visit in Part B, which is the first visit for Part C:

1. Completed all visits in Part B of the study.

Key Exclusion Criteria:

1. Known allergy to pyridine-containing substances, or any of the inactive ingredients of the prolonged-release fampridine tablet
2. Any prior history of seizures, epilepsy, or other convulsive disorder, with the exception of febrile seizures in childhood, or prior history of epileptiform activity on electroencephalogram.
3. Any form of renal impairment as defined by a creatinine clearance (CrCl) of <80 mL/min (estimated by the central laboratory).
4. Known history of cardiac arrhythmia or cardiac conduction disorders requiring medical or surgical intervention, or any clinically significant ECG abnormality (as determined by the Investigator) at the screening visit or Day 1.
5. Any prior treatment with fampridine (4 AP) or 3,4 diaminopyridine in any formulation.
6. Treatment with an investigational drug or approved therapy for investigational use within 30 days (or 5 half lives, whichever is longer) prior to the screening visit.
7. Participation in an investigational study (with the exception of observational studies) within 30 days prior to the screening visit or plans to enroll in another interventional investigational study at any time during this study.

NOTE: Other protocol defined Inclusion/Exclusion criteria may apply.