NEW YORK — Construction on a Greek Orthodox Church to replace one that was crushed in the Sept. 11 attacks has been temporarily suspended amid rising costs and questions over how donations have been managed.

The St. Nicholas National Shrine next to the World Trade Center memorial plaza was to replace a tiny church that was obliterated by the trade center’s south tower.

The new building was designed by renowned architect Santiago Calatrava, who also created the soaring white birdlike mall and transit hub nearby called the Oculus.

But unlike the transit hub, built largely with federal transportation dollars, the church is being funded through donations from the Greek government, Greek Orthodox Church members around the world, the Roman Catholic Archdiocese of Boston and the Italian city of Bari, whose patron saint is St. Nicholas.

In September, the estimated cost was $50 million. But according to The New York Times, which first reported the work suspension, the cost had jumped to an estimated $72 million and to $78 million as of earlier this month.

The stoppage was ordered by the construction company on the project.

The Greek Orthodox Archdiocese, based in New York, represents more than 500 parishes across the country with more than 1.5 million members of the church and 800 priests.