Repairs to the crumbling facade of the Renwick Gallery are expected to cost at least $4 million, which is more than five times the amount originally estimated.

The cost may eventually reach $5.5 million, Smithsonian officials testified yesterday before the House appropriations subcommittee on interior and related agencies.

Smithsonian Secretary S. Dillon Ripley said that when last year's estimate of $850,000 was determined "we had no idea how many stones would have to be replaced" on the exterior of the brownstone structure. Renovation began on the building 11 years ago.

Since then scaffolding has been erected around the street sides of the elaborately embellished building that dates from 1859. The scaffolding is necessary, said Ripley, "to keep the dust and possibly the stones from falling on people" as they pass at 17th and Pennsylvania NW.

"Meanwhile," he said, "as we examine the stones that were put there during renovation it is clear that things are worse than realized." One official suggested that as much as 80 percent of the facade replaced a decade ago may have to be replaced again.

To redo the outside, Ripley testified, "the General Services Administration committed us to what was described as an absolutely flawless technique of casting new brownstone from the dust of old stone. It turned out [not to work in most castings] and that's how we got to where we are today. It's been so frustrating I could spit tacks."

It probably will be fall before the full extent of the damage - and plans for repair - can be determined. "There are several ways we can do it," he explained. "Given the extent to which brownstone is subject to pollution anyway, maybe we should go for another stone, though that might be less attractive."

The testimony came before hearings chaired by Rep. Sidney R. Yates (D-III.) on the Smithsonian Institution budget request of $144.99 million for fiscal 1980. That would be an increase of about $6 million over this year's spending.