Members of the Cambridge City Council last night persuaded colleague Alfred E. Vellucci to postpone a vote on a proposal to stop the city's rent control board from collecting fees from landlords and tenants.

Vellucci agreed to let the measure remain on the table, where it can be considered at some future time, dropping his plan to demand a vote on the controversial question.

Councilor David Sullivan, the only tenant on the council, described Vellucci's proposal as an "attempt to strangle rent control."

Citing long delays in the processing for rent board cases, Vellucci proposed the ban on fees as a way to make the agency speed its deliberations. "Why should people have to pay all this money and wait all this time?" Vellucci asked.

He added that the fees--which are mostly in the $25 to $50 range--may be illegal since they were never explicitly approved by the city council.

But Sullivan said the council had clearly intended the fees to be levied when it passed this year's city budget, and added that the original state legislation allowing rent control to be adopted gave the rent control board enough latitude to set the charges.

"If the motion is passed, it will accomplish exactly the opposite of its intent," Sullivan said, adding "layoffs will have to occur, and the processing time will slow down even further."

City manager Robert Healy said he too believed the rent control board had the power to impose the fees, which went into effect in midsummer. "If they are illegal, why has no one challenged them?" Sullivan asked.

"The reason no one has gone to court is probably because that's an expensive thing to do," answered councilor Kevin P. Crane '71.

The rent board was allotted $430,000 in the city budget, with $133,000 to come from fees.

In other city council action last night, the council endorsed a "walk for world peace" to be held December 20 at 1 p.m. from Harvard Square to Draper Lab at Tech Square.