SAN FRANCISCO—A federal jury found on Monday that Google Inc. infringed Oracle Corp. copyrights, but its decision appeared unlikely to require Google pay a significant amount for damages.

The jury decided that when Google was developing its Android mobile phone software it made use of Oracle's Java interfaces, or essential building blocks for applications. But it was unable to decide whether that its use was protected by a fair-use doctrine that permits some limited use of copyrighted materials.

The...