The world is not doing enough to halt a "genocide" of Iraq's Yazidi, the son of the religious minority's leader said Tuesday, blaming international inaction for a recent massacre.

"We call upon the free world to immediately act," said Breen Tahseen, an Iraqi diplomat based in Britain and the son of Prince Tahseen Saeed Bek, the leader of the Yazidi people.

Speaking to reporters in Geneva as a representative of his father, Tahseen said jihadists from the Islamic State (IS) group had killed more than 3,000 Yazidi and had kidnapped 5,000 more since they first entered Iraq's northwestern Sinjar region at the beginning of the month.

The IS attack on Yazidi villages in the area of Mount Sinjar began in early August, the latest chapter in an offensive that has seen the jihadists seize large swathes of Iraqi territory, forcing minorities either to convert to Islam, flee or be killed.

Tens of thousands of Yazidi, who according to Tahseen numbered around 600,000 in Iraq before the attack, fled into the mountain.

They remained under siege with little food and water for more than 10 days, until Kurdish fighters on the ground and US air strikes eventually enabled most of them to escape.

Tahseen maintained that around 20,000 Yazidi remained on the mountain -- far more than the 4,000 to 5,000 estimated by the Pentagon.

While he hailed the efforts to help those stuck on the mountain, Tahseen lamented that little attention was being paid to the Yazidi who remain in villages in the Sinjar area, surrounded by IS fighters who regard them as heretics.

"The genocide is bigger than the mountain," he said.

He said some 4,000 Yazidi families remain in the area, including in the village of Kocho, where Iraqi officials say jihadists killed some 80 people late last week.

Tahseen meanwhile maintained that at least 300 people were killed and another 700, mainly women and children, kidnapped in the village, decrying that the United States, Britain and the UN had not heeded warnings in the days before the massacre that it was looming.

"We told them these villages were in danger," he said, urging Washington to help arm the Yazidi so they could protect themselves.

Speaking alongside representatives of the Christian community in Iraq, Tahseen also urged the UN's top human rights body to convene an emergency session in Geneva to address the abuses carried out by IS.

Non-governmental organisation UN Watch also presented a petition, signed by more than 20 parliamentarians and activists, demanding that the Human Rights Council hold an urgent meeting about the Iraq crisis.

State of play on Iraq's main frontlines
Baghdad (AFP) Aug 19, 2014 - Nearly two weeks after the United States sent warplanes back over Iraq, Kurdish and federal forces have gone on the counter-offensive in a bid to claw back the land lost to Islamic State (IS) jihadists since June.

Here is the state of play in the regions affected by the latest fighting:

MOSUL DAM AREA: Kurdish peshmerga forces and Iraqi special forces have retaken control of the Mosul dam, the country's largest. There are pockets of IS militants still fighting in the vicinity of the dam in the north of Iraq, but anti-jihadist forces have made significant progress.

TIKRIT: Iraqi government forces and allied Shiite militiamen, backed by army helicopters, launched an offensive Tuesday on the city of Tikrit (160 miles north of Baghdad), their third attempt to reclaim the hometown of executed former president Saddam Hussein.

DHULUIYA: A Sunni tribe in the southern part of Dhuluiya, 90 kilometres (55 miles) north of Baghdad, has been fighting off IS militants for weeks. There is daily fighting in the town and on Tuesday, an Iraqi air strike destroyed an IS convoy.

RAMADI: A coalition of Sunni tribes backed by government forces has been battling IS fighters to regain full control of Ramadi, the capital of the western province of Anbar. The tribal fighters have vowed to work their way up the Euphrates and take back areas near the Syrian border.

FALLUJAH: The rebellious Sunni stronghold, between Baghdad and Ramadi, has remained out of government control for eight months, long before IS launched its nationwide offensive on June 9.

JURF AL-SAKHR: The sprawling agricultural area around Jurf al-Sakhr, south of Baghdad, has been the scene of almost daily fighting pitting IS militants against the army and large numbers of volunteers keen to protect the holy Shiite cities of Karbala and Najaf further south.