WASHINGTON, June 16 (Reuters) - U.S. taxpayers may be paying too much for construction of the new headquarters of Fannie Mae, the housing finance company now in government hands, an independent government watchdog warned on Thursday.

The new Fannie Mae building in downtown Washington has seen its per-square-foot costs increase by more than 50 percent in about eighteen months, according to the watchdog's report, which said the original cost estimate for the structure was $770 million.

Fannie Mae, a leading source of mortgage finance, has operated under government control since September 2008, so any costs overruns could be felt by taxpayers, the report concludes.

"We believe there are significant financial and reputational risks from the projected costs associated with Fannie Mae's relocation of its headquarters," reads the report from the independent auditor of the Federal Housing Finance Agency (FHFA).

A board of conservators has stewarded Fannie Mae since officials effectively wiped out shareholder investment in the government takeover.

The FHFA oversees the Fannie Mae board and Thursday's report from the FHFA independent inspector general was sparked by an anonymous, hotline tip.

Melvin Watt, the director of the FHFA, defended his agency and its handling of the new headquarters building.

Fannie Mae and the regulator are still negotiating terms of the new building and the move will consolidate property holdings and save taxpayer dollars, Watt wrote.

"The sale of the properties Fannie Mae currently owns and occupies will result in substantial additional financial benefits," Watt wrote in response to a draft of the report.

The new building envisions spiral staircases and 'bridges' that transverse the building but those are part of a modern building design and not extravagances, Watt wrote.

(Reporting by Patrick Rucker; Editing by Andrew Hay)