The rival factions supporting the drive for ratification of the D.C. voting rights amendment yesterday began efforts to resolve their differences before their mutual goal is lost.

D.C. Del. Walter E. Fauntroy said "there must be a positive resolution" of the split between the newly formed voting rights service corporation and the older Self-Determination for D.C. Coalition "if we are to wage a successful campaign."

Fauntroy said he is "prepared to meet with anyone" to end the longsimmering dispute that erupted publicly Tuesday at a meeting of the coalition. Attorney Joseph L. Rauh, who criticized Fauntroy at that meeting for issuing an ultimatum for the coalition to fold into the corporation, also said yesterday that he would "break any appointment but a court date" to resolve the dispute.

Some nonpartisan organizations that are members of the coalition are resisting joining forces under the new corporation, created by the City Council, because it is headed by the city's three Democrate elected officials, Fauntroy, Mayor Marion S. Barry and Council Chairman Arrington Dixon.

Fauntroy repeated a pledge yesterday that he, the mayor and the chairman are committed to seeking a large, national board of directors representing a broad spectrum of society, including business, industry, civil rights and political organizations.

Fauntroy said the coalition's two employes, who resigned Tuesday in protest of their treatment by the corporation, were not paid on time "simply because we didn't have the money."

Part of the problem Fauntroy said was that "Joe's people didn't come through," a reference to a pledge of $10,000 to be raised from labor made by J. C. Turner president of the International Union of Operating Engineers who is a friend of Rauh's.

Fauntroy said Tuesday's meeting called by Common Cause lobbyist Richard W. Clark was premature. Fauntroy said the two groups had pledged to work for three months ending July 2 before making a decision about whether they would merge or continue as separate organizations.

Both factions agree that they must resolve their differences if the ratification drive is to succeed. Since the proposal was passed by Congress last summer six states have approved it and 10 others have rejected it. For the amendment to be ratified, 38 states must approve it by 1985.