The case of the Hazaras, whose beheaded bodies were found Saturday in the country's southeastern province of Zabul, appears to have galvanized many in war-battered Afghanistan.
Earlier in the day, about 10,000 rallied in the center of the Afghan capital, carrying coffins of the seven victims and calling for a new government that could ensure security in the country.
The shooting, which the Public Health Ministry said wounded seven people, occurred as some of the demonstrators tried to scale the walls of the presidential palace at Pashtunistan Square. It was not immediately clear if President Ashraf Ghani was inside the heavily fortified palace at the time.
"We shall revenge the blood of our brothers and sisters," he said, adding that the "enemies of Afghanistan" are trying to create disunity and "bring ethnic and sectarian violence" to the country.
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After the gunshots, many of the demonstrators dispersed but about 1,000 were allowed into the palace compound. About 30 of them were to meet with Ghani and members of his National Security Council later Wednesday to press demands for justice and security, according to organizer Lilia Mohammadi.
Kabul's deputy police chief Gul Agha Rouhani said security forces shot in the air to disperse the protesters trying to scale the palace walls. He could not confirm reports of injuries. Later, riot police took up positions at the gates as a tense calm returned.
"About 100 people were trying to get into the palace by climbing over the wall," said Ahmad Sharif, 36, who took part in the rally. He said he saw one protester hit by gunshots.