The death toll climbed to 15 on Wednesday as two more died overnight from the bomb that tore through a group of curious children in the city of Kandahar on Tuesday, police said.
In neighboring Helmand province, unidentified gunmen stopped two cars on a roadway and fatally shot 12 men in them, provincial officials said.
The violence — two years after the fall of the brutal Taliban regime — underlines the failure of the national government and its foreign backers to bring security to Afghans weary from nearly a quarter-century of conflict.
In a report to the Security Council, Annan warns that Afghanistan's peace process is "at a critical juncture."
Shootings, kidnappings and bomb attacks on soldiers and civilians have riddled southern and eastern Afghanistan in past months. The Taliban has taken responsibility for many of them.
While highlighting progress like a new currency, getting 4.2 million children back to school, human rights efforts and road building projects, Annan warned that elections planned for June "cannot be accomplished if broad geographical access is denied to the registration teams because of insecurity."
There have been several attacks in Kandahar, the focus of a U.S. plan to deploy hundreds of troops and reconstruction workers across the south and east in the run-up to the vote.
"Afghanistan has experienced a deterioration in security at precisely the point where the peace process demands the opposite," the secretary-general continued. In the past three months, he said, there were more attacks on civilians than in the preceding 20 months.
"Much of the south and southeast of the country is now effectively off limits to the United Nations," Annan reported.
The Kandahar bomb was in an apple cart, not strapped to a bicycle as initially believed, said the city's deputy police chief, Salim Khan.
The explosion was preceded by a smaller blast — which had lured a crowd of onlookers, mostly children. A battered sneaker lay amid pools of blood, mangled bicycles and glass late Tuesday.
"It was a time bomb, hidden under the apples," Khan said, adding that two more children died from their injuries overnight, bringing the death toll to 13 children and two adults. Thirty-six were wounded.
Officials and the U.S. military said they suspected the Taliban in the bombing in Kandahar, once a stronghold of the Islamic fundamentalist militia.
Overnight, U.S. forces scoured Spin Boldak, a town near the Pakistani border, for suspects in the bombing.
The blast went off on a street used regularly by U.S. military patrols.
A man arrested as he tried to flee the bombing scene on Tuesday had not told interrogators a single word, including his name, Khan said.
It remains unclear whether civilians, U.S. soldiers, guards from a nearby Afghan military barracks or others were the intended target of the bombing. Kandahar Gov. Yusuf Pashtun had been expected to pass the area near the time of the blast, officials said.
The bomb spoiled celebration of a new constitution ratified Sunday.
It wasn't clear who carried out the roadway shooting in Helmand. Provincial governor Mohammed Wali Alizai told the Associated Press that the victims were all ethnic Hazaras in an area that is predominantly ethnic Pashtuns, and suggested that the assailants wanted to stir ethnic tensions.
Meanwhile, an Afghan employee of a U.S.-based aid group, who was kidnapped in the south by suspected Taliban, was released Tuesday after being abducted a day earlier while driving along the newly refurbished Kabul-Kandahar highway in Zabul province, said Vilal Ahmad of the emergency relief group Shelter for Life.