The fighting comes a day after the US military attacked suspected anti-US and Afghan government fighters in air strikes that killed as many as 20, officials said on Monday.
Eleven fighters were killed in an hour-long firefight before dawn on Monday after attacking a government office in the Washer district of Helmand province, said Haji Muhamad Wali, a spokesman for the governor.
The district government chief and an Afghan soldier were also killed.
Another seven fighters were killed late on Sunday and early on Monday after they attacked a police checkpoint on a stretch of the Kabul-Kandahar highway that runs through southern Zabul province, said Zabul's deputy police chief, Bari Gul.
Months of fighting
A police officer at the post was also killed.
Three months of bloodshed across the south and east has left hundreds dead and sparked fears that the Afghan war is widening, rather than winding down.
US and Afghan officials warn things could get worse ahead of landmark parliamentary elections scheduled for September.
About 280 suspected anti-US and Afghan government fighters and 29 US troops have been killed since March, according to Afghan and US officials.
More than three dozen Afghan policemen and soldiers have also died, as have more than 100 civilians.
Purported Taliban spokesman Mullah Latif Hakimi claimed responsibility for the ambush of a police convoy in southern Afghanistan earlier this week and said fighters killed a district police chief and five of his men after taking them captive.
Hakimi said five other officers captured in the Thursday ambush were alive and would be put on trial.
Hakimi often calls news organisations to claim responsibility for attacks on behalf of the Taliban. His information has sometimes proved untrue or exaggerated and his link to the group's leadership is unclear.