BAGHDAD – Prime Minister Nouri al-Maliki said Saturday he would not seek a third term in office, in a sign that even Iraq’s newly installed and democratically elected government may be feeling the heat from the tumult in the streets of Cairo.

“I have personally decided not to seek another term in office after this one, a decision I made at the beginning of my first term,” al-Maliki said in an interview with Agence France-Presse.

Iraq’s new constitution does not set term limits for the prime minister, but al-Maliki said he would seek a constitutional amendment restricting the number to two.

Al-Maliki began his second four-year term in December, after spending 10 months fending off a challenge from the secular leader Ayad Allawi, whose bloc won two more seats in parliament than al-Maliki’s in nationwide elections in March.

His comment coincides with an upsurge of scattered protests across the country demanding better services, jobs and an end to corruption, apparently inspired by the pro-democracy demonstrations under way in Cairo and those that toppled Tunisia’s long-serving president last month.

Police in Najaf broke up an attempted demonstration in support of the Egyptian people Saturday after the governor of Najaf refused to grant permission. The gathering was organized by the Najaf office of Iran’s supreme leader, Ayatollah Ali Khamenei, according to police Col. Ali Jarayo.

On Thursday, police injured four people when they fired into the air to quell a crowd of about 700 stone-throwing demonstrators protesting poor services in the southern province of Diwaniyah, according to provincial officials there. A second protest in the province Friday was dispersed without incident.

No one is calling for the overthrow of the al-Maliki government, chosen in an election judged largely free and fair. The next election isn’t due until 2014.

But the protests are a reminder that even democratically elected governments aren’t immune to popular unrest if they don’t provide jobs and services. Six years after Iraq’s first democratic election, most Iraqis endure long hours daily without electricity, water shortages are common and jobs are scarce.