A series of five explosions and gunfire killed at least 35 people, including police forces in southern city of Kandahar, an interior ministry spokesman said on Sunday.
The Taliban called the attacks a reaction to the NATO commander's warning about an imminent military offensive in the region.
Several insurgents equipped with suicide vests and assault rifles targeted several parts of Kandahar city Saturday night, killing "35 people, including 13 brave policemen of this country", Zamarai Bashary, an interior ministry spokesman, said in Kabul Sunday.
He said 57 other people, including 17 police forces, were injured in the attacks. Around 25 shops and more than 40 houses were also destroyed or damaged.
The attack came amid warnings by US Gen Stanley McChrystal and other NATO officials about a spring offensive in Kandahar. That would follow the biggest military offensive by Afghan and NATO forces since the ouster of Taliban regime in late 2001, in Marjah district of neighbouring Helmand province.
"The attacks were a reaction to McChrystal's warning about a new operation in Kandahar province," Taliban spokesman Qari Mohammad Yousif Ahmadi said in a statement posted at the rebel website. "Our Mujahideen showed to NATO and American forces that the start of that operation would cost them heavily."
"Mujahideen have full preparation and ability to carry out successful attacks in all parts of Kandahar, even in the heart of the city," he said.
Ahmadi claimed by phone earlier from an undisclosed location that the attacks in Kandahar, the second most important political city in the country, left nearly 50 Afghan and foreign forces dead and 70 others were wounded.
Tooryali Wesa, Kandahar's provincial governor, said Sunday that only seven police were among those killed in the attacks and another eight were injured, while the rest were all civilians.
Seven women and three children were also among the dead, most of them killed when one of the bombers detonated his explosives near a wedding hall in the city, he said.
The coordinated assaults began when a suicide bomber tried to enter the central jail on the western outskirts of Kandahar in a vehicle loaded with 700 kg of explosives, Wesa said.
Other militants targeted the police chief's residence, and two markets in the city. Witnesses said rocket-propelled grenades were also fired, and gunfire rang out in several sectors. Electricity supply was also cut following the blasts.
Wesa said he was talking to central government about increasing security in Kandahar, the birthplace of the Taliban movement and the headquarters for its leader, Mullah Mohammad Omar, until late 2001.
Four Pakistani construction workers and one Afghan were injured Sunday when a roadside bomb hit their vehicle in Kandahar city near the Pakistan consulate, the governor said.
That attack came a week after four Pakistani workers and their Afghan colleague were killed when unknown gunmen attacked their vehicle in another part of the city.
About 15,000 Afghan and NATO forces began Operation Mushtarak, a local word for "together", in Marjah and the neighbouring Nad Ali district of Helmand province in mid-February.
NATO officials said that operation is a prelude to a bigger offensive planned for Kandahar in the spring. US officials have said that most of the 30,000 additional US troops scheduled to arrive in the country by summer will be stationed in Kandahar.
The Afghan defence ministry said Sunday that troops backed by NATO troops killed six foreign fighters allied with Taliban insurgents in Asmar district of eastern province of Kunar Saturday.
A senior Taliban commander, Muhammad Yah, was killed in a separate Afghan-NATO operation in Lashkargah, the capital city of Helmand province Friday, the NATO military said Sunday.
"Muhammad Yah was known to have planned and facilitated both improvised explosive device attacks and to have directed suicide attacks around Lashkargah," it said. "While he primarily targeted Afghan forces and international partners, his attacks often killed or injured innocent Afghan civilians."