President Reagan yesterday signed legislation authorizing the Smithsonian Institution to build a new center for African, Near Eastern and Asian art on the Mall. The act paves the way for congressional appropriations committees to decide whether to fund the project for the next fiscal year.

"It's obviously an encouraging step forward," said Charles Blitzer, assistant secretary for history and art at the Smithsonian. "We're very pleased."

The Smithsonian estimates the total cost for the center at $75 million, half of which the institution will raise. Congress had already approved $960,000 for planning this fiscal year. The question now is whether it will appropriate another $36.5 million for the next fiscal year. The Smithsonian is already listed for another $156.1 million in the proposed budget for fiscal 1983.

If funding is approved and the Smithsonian raises its share, the center could be completed by the end of 1986, estimates Blitzer. It would sit between the Freer Gallery of Art and the Arts and Industries Building on the Mall. There will be two small pavilions above ground but 90 percent of the museum will be situated below on three levels, connected to the Freer. Previous plans to design the pavilions in Japanese and African motifs have been abandoned. "It was a little too World's Fair-looking," said Blitzer.