The body found near Kandahar in Afghanistan is that of K Suryanarayan, 41, the abducted Indian engineer, the office of the Indian prime minister, Mamohan Singh, said on Sunday.
Suryanarayan was kidnapped on Friday with his driver after armed men stopped their vehicle on a road in Zabul province.
Taliban insurgents said on Saturday they took both men and vowed to kill the Indian unless India withdrew all its workers from Afghanistan in 24 hours.
"We found the body, beheaded, in a ditch by a road, about 10km from where he was kidnapped," said Mohammad Mir, a district police chief in the southern province of Zabul.
Mir said there was no word on the fate of the Afghan driver.
Suryanarayan appeared to have been killed on Saturday evening and his body had been taken to Ghazni province, he said.
The Indian prime minister also condemned what he called the Taliban's "inhuman act", his spokesman Sanjaya Baru told AFP.
"The prime minister has expressed his grief and sorrow" over the killing ... Singh has spoken to the chief minister of Andhra Pradesh state and asked him to take care of Surayanarayan's family, Baru said.Taliban spokesman Qari Mohammad Yousuf said by telephone Suryanarayan had been shot dead on Saturday evening while trying to escape.
The Taliban claimed to have kidnapped both men and said on Saturday afternoon that the Indian man would be killed unless India withdrew all its workers from Afghanistan in 24 hours.
The threat came as violence in the south of the country left 11 insurgents and three Afghan policemen dead.
The threat to kill Suryanarayan was made by a Taliban spokesman, Yousuf Ahmadi, in a telephone call to AFP.
Suryanarayan was working as a contractor for Afghan mobile phone network Roshan.
It has been decided "that if all Indian companies, engineers and workers in Afghanistan do not get ready to leave the country in the next 24 hours, starting 6pm (1330 GMT) today, we will kill this Indian engineer".
The purported spokesman also said the Taliban leadership had concluded that the Indian engineer was spying for the Americans.
"If all Indian companies, engineers and workers in Afghanistan do not get ready to leave the country in the next 24 hours ... we will kill this Indian engineer"
purported Taliban spokesman
India has close relations with Afghanistan and is involved in numerous aid and reconstruction projects.
Security is a big worry in Afghanistan with Taliban attacks mounting as Nato prepares to double its peacekeeping operations and the US hopes to cut its forces there by several thousand.
Elsewhere, nine Taliban insurgents were killed during fighting that raged overnight on Friday into Saturday, while 12 insurgents, including top commanders, were captured in a joint Afghan-coalition operation in Panjwayi, a western district in the southern Kandahar province, according to Asadullah Khalid, the regional governor.
Also on Saturday morning, about 50 Afghan soldiers and police attacked a Taliban camp hidden in mountains in the district of Kajaki, about 100km north of the Helmand capital of Lashkar Gah, a local Afghan army commander, General Rahmattalluh Roufi, said.
After a one-hour battle, Afghan forces ventured into the mountains and found caves that had been used by the Taliban.
The bodies of two slain fighters were found, along with several machine guns.
Taliban insurgents concealed in mountains also fired on a vehicle carrying four policemen late on Friday, killing three of them and wounding the other on a remote road outside the southern Helmand provincial town of Baghran, said police official Haji Rafiq Khan.