BUDAPEST, Hungary — Thousands of Hungarians took to the streets on Saturday, calling for Prime Minister Viktor Orban to step down just days after he was elected to a third consecutive term in office.

The protests, held in Budapest and several other cities, are unlikely to prompt the newly elected government to change course, but they reflect the deep divisions in this Central European country that has been at the forefront of a regional drift away from liberal Western values.

“Democracy is just inconceivable without the rule of law and free media,” said one protester, Levente Biro, 24. “We’ll march as long as needed.”

The demonstrations came a week after Mr. Orban and his Fidesz party secured a convincing victory in national elections, their power seemingly on the ascent. The political opposition is in disarray, civil society is under attack and the news media is almost fully under the control of the state.