Three US troops were slightly wounded when a bomb exploded near their armored Humvee in Paktia province on Sunday, said US military spokesman Col. James Yonts.
A Taliban spokesman, meanwhile, claimed his fighters had assassinated a kidnapped Afghan police chief and five of his men for collaborating with the US-led coalition.
Eleven rebels were killed in an hour-long firefight before dawn Monday after attacking a government office in the Washer district of Helmand province, said Haji Mohammed Wali, a spokesman for the governor. The district government chief and an Afghan soldier also died.
Seven rebels were killed late Sunday and early 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. A policeman manning 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 rebels and 29 US troops have been killed since March, according to Afghan and US officials. More than three dozen Afghan police and soldiers also have died, as have more than 100 civilians.
Yonts warned that foreign militants backed up by networks channeling them money and arms had come into Afghanistan to try to subvert legislative elections in September. He said that for "operational security reasons" he could not identify the networks or who was backing them.
Afghan Defense Minister Rahim Wardak told The Associated Press last week that intelligence indicated al-Qaeda had slipped at least have a dozen foreign agents into the country, two of whom had already detonated themselves in suicide attacks
On Sunday US aircraft opened fire on a group of suspected Taliban along a narrow footpath in the high mountains northwest of Gereshk, in southern Helmand province, after rebels had pinned down a coalition ground patrol with rocket and small-arms fire.
"Initial battle-damage assessments indicate 15 to 20 enemies died and an enemy vehicle was destroyed," the US Army said in a statement Sunday. No Americans were injured.
Military spokesman Lt. Col. Jerry O'Hara added a warning to the insurgents.
"When these criminals engage coalition forces, they do so at considerable risk," he said. "We are not going to let up on them. There is not going to be a safe haven in Afghanistan."
O'Hara told The Associated Press that additional US and Afghan forces had been sent to the scene and the numbers of rebel dead could rise.
Elsewhere in Helmand on Sunday, gunmen shot to death three men -- a judge, an intelligence worker and an employee of the provincial education department, said Wali, the governor's spokesman.
He said it was not clear whether the Taliban or some other armed group was behind the Saturday night attack.
And in Kandahar, rebels fired three rockets into the city center early Sunday, jolting residents but causing no casualties.
Purported Taliban spokesman Mullah Latif Hakimi claimed responsibility for the ambush of a police convoy in southern Afghanistan earlier this week and said insurgents had 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. He said the men would face trial.
Hakimi often calls news organizations to claim responsibility for attacks on behalf of the Taliban. His information has sometimes proven untrue or exaggerated and his exact tie to the group's leadership is unclear.