The federal government authorized a multimillion-dollar contract Friday to continue work on a massive Department of Veterans Affairs hospital in Colorado that is more than $1 billion over budget and has been plagued by delays, bad management and cost overruns.

The U.S. Army Corps of Engineers awarded Kiewit-Turner LLC, the existing prime contractor on the project, a $570 million contract to continue work on a VA health-care campus in Aurora, Colo., near Denver.

Kiewit-Turner,...