WASHINGTON -- The White House said Thursday it was seeking ways to include same-sex marriages, unions and partnerships in 2010 Census data, the second time in a week the administration has signaled a policy change of interest to the gay community.

The administration has directed the Census Bureau to determine changes needed in tabulation software to allow for same-sex marriage data to be released early in 2011 with other detailed demographic information from the decennial count. The bureau historically hasn't released same-sex...