D.C. City Council Chairman Arrington Dixon has invited seven Democratic council members to a secret dinner meeting at his home next Tuesday, sparking sharp criticism from four of the council members who were not invited.

Dixon's letter, writter on a council letterhead and hand-carried to the invitees, indicated that the meeting would "explore . . . and in some cases finalize" such public matters as the city budget. But last night he insisted the meeting would be political, to explore support for the reelection of President Carter.

One of the five who was not invited, John L. Ray (D-At Large), scoffed at Dixon's explanation and said "the chairman can't even tell a good story . . . He has clearly demonstrated he does not have the qualifies -- the good judgment -- necessary to preside over the City Council."

Ray was joined in a critical letter to Dixon by Betty Ann Kane (D-At Large), Hilda Mason (Statehood-At Large) and Nadine P. Winter (D-Ward 6). Ray said he was not able to contact the fifth member who got no invitation, Jerry A. Moore Jr. (R-At Large).

Ray, Kane and Winter all are members of a group that has endorsed Sen. Edward M. Kennedy (D-Mass.) for the Democratic presidential nomination.

In their letter, drafted by Ray, the four protesting members charged that it would be "a clear violation of the council rules and the sunshine laws to be discussing and finalizing council business at a secret meeting in your home . . . "

Dixon's invitations made no explicit mention of politics, saying the dinner meeting would deal with "budget . . . staffing . . . programs and grants . . . and activities of considerable importance to all of us enjoying elective office."

"I chose the setting of my home with the hope of fostering the confidentiality of this occasion," Dixon wrote. He lives at 5227 West Beach Ter. NW.

After word spread about the invitations, Dixon invited reporters into his office and insisted that the meeting would be held "to discuss the impact of our involvement in the 1980 election." He said an unidentified representative of the Carter campaign would attend.

Dixon said neither he nor his wife, Sharon Pratt Dixon, the Democratic national committeewoman for the District, has endorsed any presidential candidate.