BAGHDAD — Bombings that hit markets and other insurgent strikes primarily targeting Iraq’s Shi’ite community killed 31 people on Saturday, challenging government efforts to promote a sense of stability by preventing attacks during a major Muslim holiday.

The bloodshed underscored the difficulties facing Iraq’s leadership as it struggles to keep its citizens safe. Authorities had increased security in hopes of preventing attacks during the four-day Eid al-Adha celebrations, when people are off work and families gather in public places.