Jones told NBC on Saturday that "we feel that God is telling us to stop" the Quran burning, which had stirred outrage among millions of Muslims and others worldwide.
"We're not going to go back and do it," Jones said, referring to the planned burning. "It is totally canceled."
But in a country where most people have limited access to newspapers, television and the Internet, most Afghans were unaware of Jones' decision. The Taliban have been distributing pamphlets decrying Jones' plans, claiming they showed the Americans were in Afghanistan to wage war against Islam.
In Logar province near the capital of Kabul, police fired warning shots to prevent protesters from storming the governor's residence in the provincial capital of Puli Alam, officials said. Villagers set fire to tires and briefly blocked the main highway to neighboring Pakistan, according to provincial spokesman Din Mohammad Darwish.
Nabi Charkhi, the deputy provincial police chief, estimated the crowd at more than 10,000. Witnesses said Taliban agitators were among the crowd. The witnesses spoke on condition of anonymity out of fear for their personal safety. At least four people were injured, police said.
"All these youths, elders have gathered here because of the Quran," said Amir Gul, a Logar protester. "We will continue our protest until they change their decision about burning our holy book and we will not keep silent."
Another protester, Abdullah Hanafi, said that if copies of the Quran are set ablaze, the government should join forces with the Taliban "to force all the invaders from our country."
In the northeastern province of Badakhshan, several thousand people took to the streets in three separate districts, although the demonstrations were generally peaceful, according to provincial police chief Gen. Agha Noor Kemtuz.
Several hundred protesters rallied Saturday outside the giant Bagram Air Field, a major NATO base north of Kabul. The protest ended peacefully after about an hour, Afghan officials said.
At least 11 people were injured in similar protests across Afghanistan on Friday.
Last Tuesday, the top U.S. and NATO commander, Gen. David Petraeus, warned that images of the burning of a Quran "would undoubtedly be used by extremists in Afghanistan -- and around the world -- to inflame public opinion and incite violence."
NATO Secretary-General Anders Fogh Rasmussen echoed those sentiments, saying any burning "would be in a strong contradiction with the all the values we stand for and fight for."
A pamphlet circulated by the Taliban among Afghan refugees in the Pakistani city of Quetta called the burning of the Quran "an immoral and stupid crime"
"And it is Americans who are doing this," the pamphlet said.
"This is the brutal policy of the enemy of Muslims."
In 2005, 15 people died and scores were wounded in riots in Afghanistan sparked by a story in Newsweek magazine alleging interrogators at the U.S. detention center in Guantanamo Bay placed copies of the Quran in washrooms and flushed one down the toilet to get inmates to talk. Newsweek later retracted the story.