CAIRO — Tens of thousands of protesters joined in anti-government marches across Sudan on Saturday in what organizers said was one of the largest turnouts in more than three months of demonstrations calling for embattled President Omar al-Bashir to step down.

The demonstrations began in December over price increases and food shortages, and quickly escalated into calls for Mr. al-Bashir’s resignation, posing one of the biggest challenges yet to his nearly 30-year rule.

The rallies are being led by the Sudanese Professionals Association, an umbrella group of independent professional unions.

Footage posted online showed thousands of protesters, mostly young people, marching toward the military’s headquarters in the capital, Khartoum, demanding the army’s support and chanting: “One people, one military,” and “Freedom.”