Washington (CNN) -- The Washington Monument was closed indefinitely as engineers study damage and ways to repair cracks at the top of the capital's iconic structure caused by the 5.8-magnitude earthquake that rattled the East Coast this week.

Tuesday's quake caused a 4-foot crack in the pyramidion at the top of the 555-foot obelisk and several pieces of mortar fell inside the monument's observation area during the earthquake, a National Park Service spokesman said.

An outside structural engineering firm is conducting a thorough damage assessment, and the monument may not be reopened to the public until after any necessary repairs are completed, the spokesman added.

"It could be awhile and the most important thing is the visitors' safety is key, is paramount, is chief and we're not going to risk anyone going in and becoming injured," National Park Service spokesman Bill Line said.

The Washington National Cathedral also was closed after sustaining what its staff described as "substantial damage," including cracks in the building's limestone blocks and broken pinnacles on its towers.

Most federal buildings and monuments in Washington have reopened, including the Lincoln and Jefferson memorials.

CNN's Jim Acosta contributed to this report.