Thousands of Afghans have fled to Ghazni city to escape fighting in two Hazara-dominated districts, with some describing the violence on Tuesday as the worst they had seen in the 17-year conflict.

The Taliban have been battling members of Afghanistan's special forces and ethnic Hazara militia in the previously safe districts of Jaghori and Malistan in the southeastern province of Ghazni for nearly a week.

Hundreds of people, including civilians, militia, commandos and militants, have been killed, according to figures provided by locals and government officials.

Many families have fled to the provincial capital, some leaving their homes in the middle of the night and travelling on side roads to avoid Taliban checkpoints.

"We were scared, other people were fleeing so we decided to leave too," said a woman called Zainab, who drove with her five children for 12 hours on dirt roads from her home in Jaghori district to Ghazni city.

"We have never seen this kind of war and my children and I were scared," she told AFP, adding that her husband had stayed behind to protect their property.

Around 2,000 families displaced by the fighting are living in mosques and hostels in Ghazni city, said Abdul Haleem Noori, director of the Afghan Red Crescent Society in Ghazni.

Others are staying with relatives as they wait out the fighting.

Afghan security forces have stepped up ground and air offensives in the restive region, and United States forces also have launched air support, including aerial surveillance.

The escalation in fighting comes amid a flurry of diplomatic activity to convince the Taliban to negotiate an end to the war.

Jaghori district "is surrounded by Taliban and there are a lot of them", Mohammad Ali told AFP in a mosque where he is staying with nine family members.

"They were very well equipped with night-vision goggles and heavy weapons."

Fighting in the area has been ongoing since Wednesday.

There are growing fears the violence could be rooted in ethnic or sectarian differences.

Most Hazaras belong to the Shia sect of Islam.

The Taliban, which are Sunni and largely ethnic Pashtuns, have been accused of committing human rights violations against the group during their oppressive 1996-2001 rule.

As displaced families continued to arrive in Ghazni city on Tuesday, provincial police spokesman Ahmad Khan Sirat told AFP the "situation is under control".

"Commando forces have been deployed in both Jaghori and Malistan," Sirat said.

"We have reports of sporadic fighting."

The Afghan Red Crescent Society has dispatched food, warm clothes and medicine to hundreds of families still in Jaghori and Malistan districts.

The fighting has angered many Hazaras, who blame the government for failing to protect the minority ethnic group.

Hundreds of demonstrators took to the streets of Kabul in the past two days to demand the deployment of military reinforcements to the Hazara districts under Taliban attack.

A suicide bomber blew himself up near the protesters on Monday, killing at least six people and wounding 20 in an attack claimed by the Islamic State group.