Another leaflet, in Kandahar city, said: "This is to inform respected residents that you must not participate in the elections so as not to become a victim of our operations, because we will use new tactics."
The threats came as hospital sources in Kandahar said one person was killed and another eight injured on Sunday after three mortars were fired into the centre of the city.
The attack happened not far from a pro-Karzai rally in the city's main sports stadium.
Qari Yousuf Ahmadi, a Taliban spokesman, confirmed the threatening leaflets were authentic and that commanders were ordering a boycott of the vote.
"We are using new tactics targeting election centres... We will accelerate our activities on election day and the day before," he said.
Later, a rocket attack in the southern province wounded two children working in a shop in Kandahar city.
The leaflets, which mark the first direct Taliban threat to attack polling sites, follow a suicide blast in Kabul.
At least eight people were killed in the attack, just outside the headquarters of Nato's International Security Assistance Force (Isaf) in the Afghan capital on Saturday.
Nick Clarke, Al Jazeera's correspondent in Kabul, said: "It's just four days until Afghanistan's presidential elections, and I can tell you things are very much on edge here."
The Taliban has upped its offensive ahead of the country's elections, due on August 20.
Election officials have said fears of violence could prevent hundreds of polling stations from opening and that voting was unlikely in nine of the 365 districts.
Hamid Karzai, the president of Afghanistan, took part in a live television debate with two of his main rivals on Sunday.
Karzai, considered the frontrunner, took to the stage with Ramazan Bashardost, an independent candidate, and Ashraf Ghani, the former finance minister.
Abdullah Abdullah, the former foreign minister, pulled out of the debate, which was aired on state broadcaster Radio and Television Afghanistan (RTA), an announcer said.
|Karzai made many promises to the Afghan people that concerned foreign forces [AFP]
James Bays, Al Jazeera's correspondent based in Afghanistan, said: "Karzai was pressed on many issues and it was a good platform for him to say what he was going to do after nearly eight years in power.
"If he is re-elected, he said he was going to make some big changes and the most significant points concerned foreign forces.
"He said that there will be no military operations by international forces if they were not first permitted by Afghans.
"He said he would not allow international forces to search Afghan homes. And he said he didn't want any Afghans in the future to be held in jails run by foreigners.
"So that means that controversial prison base at Baghram airport - which lots of human rights organisations have been talking about - will have to close."
A good turnout in Thursday's presidential election will be crucial for the vote to be considered legitimate.