Afghan officials said insurgents stormed a police station in the southern city of Lashkar Gar late on April 19, wounding two officers and a civilian.
Lashkar Gah is the capital of Helmand Province, a stronghold of the Taliban.
Elsewhere, gunmen kidnapped at least a dozen Afghan mine clearers in eastern Paktia Province.
The provincial police chief said the clearers had been working without police or soldiers protecting them at their own request.
No group immediately claimed either attack.
The attacks came a day after a suicide bomber in Jalalabad killed at least 35 people and wounded around 125.
President Ashraf Ghani attributed that attack to the Islamic State extremist group, without revealing the source of his information.
Also on April 19, the United Nations said that Afghanistan's women are being let down by the country's justice system as most complaints of domestic violence were dealt with through mediation rather than prosecution.
In a new report, it said that only 5 percent of surveyed domestic violence cases were resolved through the judicial system, resulting in criminal prosecution and punishment for perpetrators.
The UN's assistant secretary-general for human rights, Ivan Simonovic, said women often choose mediation to resolve complaints of violence, partly because they lack faith in the justice system.
"The interviews with women and girls subjected to violence revealed that negative perceptions of the justice system as slow, corrupt, and distant continued to discourage women from pursuing criminal prosecution of the perpetrators," Simonovic said.
He added that access to justice for women who suffer violence needs to be improved.
Afghanistan is regularly named as one of the worst places in the world to be a woman.
Constitutional guarantees of equal rights and protection from violence are rarely applied in practice.