BAGHDAD — For a few brief hours Tuesday, three dozen spectators — journalists, local politicians and their guards — gathered at the National Museum of Iraq here, their voices echoing through its vast, darkened halls. It was one of the few times outsiders had been allowed inside since Baghdad fell, looters stripped the galleries of some 15,000 Mesopotamian artifacts, and the museum became a wrenching symbol of the losses of the war.

Aside from a brief opening in late 2003, when officials and other guests were invited in, the museum has been shuttered since the invasion. But there has been a great push to reopen it of late. Its directors have managed to recover 4,000 missing pieces, among them gems, Islamic coins and carved stones. The pace of recovery picked up as word spread that rewards were offered for items returned.

Still, the executive director, Amira Eidan, said Tuesday that she could not forecast when the museum might reopen again because restoration efforts had been slowed by insufficient financing. The cost of recovering the artifacts has consumed the bulk of her museum’s budget, and pieces sometimes have turned up at foreign auctions and been too expensive or difficult to retrieve, she said.