BAGHDAD—The Islamic militants who seized large swaths of Iraq last month have threatened Christians with death if they don't convert to Islam, pay a tax or flee insurgent-held areas by Saturday.

Insurgents from the group that calls itself Islamic State made the threat Thursday night over mosque loudspeakers and from cars driving through city streets, residents said. They reiterated the declaration in a flier distributed to worshipers who attended Friday prayers.

Most of the Christians in Iraq's second city of Mosul and its environs fled last month when the area fell to the Sunni Muslim extremists. But the warning has raised concerns about the fate of thousands who remained behind, along with hundreds of churches and the rich cultural heritage of one of the world's oldest Christian communities.

Iraqi Christians are thought to make up little more than 5% of the population of some 23 million people. Once one of the more vibrant Christian populations in the Middle East, 10 years of war and the rise of Islamic extremism already induced much of the country's Christian minority to emigrate.

The threat comes nearly six weeks after insurgents seized the northern city of Mosul. It shows how the shadowy Islamic State is imposing its austere interpretation of Islamic law by gradually tightening its authority over a population that, only weeks ago, had seemed to welcome the militants' arrival.