A suicide bomber killed 13 people at a Shiite mosque in central Baghdad Tuesday while violence elsewhere in Iraq left four dead, the latest in a protracted surge in bloodshed.

The bomber blew himself up at the entrance to the mosque in the capital's Shorja district as worshippers were performing ablutions ahead of midday prayers.

Another 28 people were wounded in the blast at the Abu al-Timan Husseiniyah, security and medical officials said.

Elsewhere in the capital, roadside bombs in the Sadr City and Dura districts left two people dead.

Bombings in the main northern city of Mosul killed another two people.

Violence has surged in the past year to its highest level since 2008, while anti-government fighters control the city of Fallujah, a short drive west of Baghdad and parts of another.

The authorities have trumpeted security operations against militants and blamed external factors such as the civil war in neighbouring Syria for the surge in violence.

But analysts and diplomats say the Shiite-led government has failed to do enough to reach out to the disgruntled Sunni Arab minority to undercut support for militancy.