D.C. City Council Chairman Arrington Dixon yesterday agreed to pay his nominee for secretary of the council, John P. Brown, $10,000 less than originally planned in order to win tentative approval of Brown's confirmation.

Under a compromise worked out with council members, Brown will be paid $41,000 a year. His predecessor was paid $50,112, and the post is still authorized at that higher lever.

Such an appointment would normally win easy council approval. But several council members used the vote to express their dissatisfaction with Dixon's management of the council staff. Members have complained that the staff is overpaid and underworked, and that Dixon seems oblivious to the city's overall financial problems.

The District government currently faces a potential budget gap of $172.4 million. On March 1, Mayor Marion Barry ordered a freeze on most hiring and promotions in the city government. However, the council's staff was not affected by the order.

Dixon told council members yesterday that the position of secretary was crucial and said that despite the overall financial squeeze, the council has remained within its own budget.

"The council as an institution is not in any fiscal crisis," said Dixon, who has asked Congress to include funds in the 1981 D.C. budget for 18 additional council staff members. Currently, the council has a staff of 130.

The secretary is essentially chief administrator of the council, with jurisdiction over the central staff and responsibility for the council's day-to-day operations.Brown, formerly Dixon's executive assistant, has filled the duties of secretary since Ruth O. Robinson left the post last November after a dispute with Dixon over staff appointments.

Robinson was paid $50,112 a year as secretary. In the past, other top council staff positions -- including those of general counsel and legislative counsel -- have and still do carry salaries much higher than those of regular council members.

Membership on the City Council is technically a part-time job, though most members say they work at it full-time. Salaries of council members range from $32,000 to $37,000. Dixon, the only council member authorized as a full-time employe, earns $47,500 a year.

Last week, six members of the council introduced legislation that would prohibit any staff member from making more than $37,500. The measure was designed to decrease city spending and to carry out the personal wishes of some council members that aides should not earn more than the elected representatives.

"We've been over this time and time again in executive session," said council member Betty Ann Kane (D-At Large), who along with three others voted against the Brown appointment. "Arrington sees it as a competition with the mayor. He says, 'Look, the mayor has all these high-paid people, why can't we?'"

"I don't particularly care who holds the office of secretary," said council member John A. Wilson (D-Ward 2). "John Brown is a fine individual of impeccable character. But I will not pay anybody who works for this council more than $37,500. That is all I am willing to pay, period. I don't care if he or she can walk on water."

Council member Charlene Drew Jarvis (D-Ward 4) supported Dixon. Jarvis said she was "not willing to hostage the appointment of Mr. Brown" to the budgetary concerns of the other members.

Voting against confirmation were council members Wilson, Kane, Polly Shackleton (D-Ward 3) and John Ray (D-at Large). The confirmation was supported by Dixon, Jarvis, David A. Clarke (D-Ward 1), William R. Spaulding (D-Ward 5), Willie J. Hardy (D-Ward 7), Wilhemina J. Rolark (D-Ward 8), Hilda Mason (Statehood-At Large) and Jerry A. Moore Jr. (R-At Large), Nadine P. Winter (D-Ward 6) was absent.

The vote yesterday was taken by the council meeting as a committee of the whole. Final action is expected later this month.