The officials said more than 200 fighters were in combat with 250 police and Afghan soldiers, as well as US troops - making it the biggest and deadliest battle in months.
The bloodshed underscores the massive challenge that will face thousands of British and Canadian troops in the next few months as they relieve American forces in southern Afghanistan, where anti-government sentiments remain strong.
According to Khan Mohammed, a police chief in Helmand province, American and British war planes bombed suspected Taliban members on Friday at midnight, killing eight people. The bodies were left on the ground where they fell, he said.
Amir Mohammed Akhund, the province's deputy governor, said the men were fleeing fighting that started hours earlier with a mountain ambush of a police convoy and ended with 16 militants and six police dead, and scores wounded.
A US military statement said eight suspected insurgents were detained.
Akhund said another group also fleeing the initial clash attacked a government office in Helmand's Musaqala district early on Saturday, killing the government chief and wounding four policemen.
Later in the day, another group attacked the government office in neighbouring Nauzad district, setting off a two-hour gun battle that left one policeman and three suspected Taliban fighters dead, he said.
The fighting prompted dozens of families to leave their villages.
Militants used remote-controlled
bombs to attack convoys
Sher Mohammed, a police officer, reported that a remote-controlled bomb was used to attack a police convoy in Kandahar, the main city in southern Afghanistan and a former Taliban stronghold.
A district police chief in the convoy was unhurt, but a woman and a child who were walking in the area were killed, and three other passersby were wounded, he said.
Asadullah Khalid, a Kandahar governor aide, said also in Kandahar, a Taliban commander, Abdul Samad, was killed by border forces as he tried to enter illegally from neighbouring Pakistan.
Ten other fighters with him fled back across the frontier. The US military confirmed that it was involved in fighting on Friday, but spokesman Lieutenant Mike Cody said he had no reports of involvement on Saturday.
The violence comes after an unprecedented spate of suicide bombings that have added a new security threat in the country four years after the ouster of the Taliban.
Fighting last year left 1600 people dead, the highest death toll since 2001, as militants stepped up their campaign against the US-backed central government.
An donors' meeting in London
has pledged $10.5 billion in aid
The Afghan authorities blame much of the violence on foreign militants.
An Iraqi was caught this week trying to enter the country - and after interrogating him, officials said they believe a large group of Arab al-Qaida militants are on their way in.
The latest fighting comes just days after an international donors' conference in London ended with $10.5 billion in new aid pledged - much of it for improving security.