ISTANBUL—Turkey’s government blamed Islamic State for a suicide bombing in a Kurdish border town that killed at least 31 people, one of the worst cases of spillover violence from the four-year-old war in neighboring Syria.

The attacker targeted a cultural center in the town of Suruc where some 300 members of socialist youth groups from across the country were meeting Monday to prepare rebuilding projects in the Syrian city of Kobani, just across the border. Authorities said they suspect a suicide bomber on foot waded into...