The European Union, which has been coaxing Serbia into a historical reckoning about its bloody role in the Balkan wars of the 1990s, gave a cautious welcome Wednesday to a declaration by the Serbian Parliament that condemned the 1995 massacre of 8,000 Muslims in Srebrenica. But it warned that what amounted to reluctant, latter-day contrition about the worst massacre in Europe since World War II was insufficient if Serbia wanted closer ties with the bloc.

For that, the E.U. foreign policy chief, Catherine Ashton, indicated, Serbia must hand over Gen. Ratko Mladic, the Bosnian Serb military commander indicted more than 15 years ago on war crimes charges but still on the run.

After 13 hours of heated debate, the Serbian Parliament late Tuesday passed a resolution that apologized for Srebrenica and acknowledged that more could have been done to prevent the tragedy, but fell short of calling the killings a “genocide.”...