Media reports said around 30 gunmen stopped four cars on the road between Kerman and Bam, and bound the bodies of 12 occupants before shooting them dead.
State television showed the corpses of the victims, whose hands were tied behind their backs, dumped in a trench.
Only a young boy aged 11 was spared, but he is reportedly severely traumatised after being tied to a post and forced to watch the shootings.
A deputy of Kerman province's governor general, Abolqasem Nasrollahi, said six of the attackers were killed in a shootout as they fled east.
He also told the Fars news agency that the 15 to 20 militants were dressed in police uniforms.
Iranian Interior Minister Mostafa Pour Mohammadi told ISNA news agency that the remaining attackers are "being pursued and are unlikely to cross the border."
The attack has led to a petition signed by more than 100 MPs calling for a motion to impeach the interior minister.
Iranian police later said the attack was claimed by Jundallah, or the Army of God, in a phone call, however a BBC report said the group's leader has denied involvement in the killings.
Jundallah is a shadowy Sunni militant group believed to be based across the border in southwestern Afghanistan, and has been blamed for a string of armed incidents along Iran's borders with Afghanistan and Pakistan. The motive for the attack is not clear.
Attacks intensify
Mr Mohammadi said since the new Iranian year began on March 21, Iran has experienced an "intensification" of militant activity in its sensitive border areas.
These include activities blamed on Jundallah in the southeastern provinces of Kerman and Sistan-Baluchestan, ethnic Kurdish unrest in the west along the border with Iraq's Kurdish region, and ethnic Arab unrest in the oil-rich province of Khuzestan in the southwest.
In mid-March, members of Jundallah allegedly entered Iran and killed 22 people, and shortly afterwards Iranian troops said they had killed eight rebels.
On April 9, press reports said "rebels", although they were not identified as Jundallah fighters, had killed two Iranian army officers and seriously wounded a senior religious official in Sistan-Baluchestan province.
Sunnis form the majority in Baluchestan, although Shiite Islam is Iran's official religion.
Southeastern Iran is a major thoroughfare for narcotics smuggled from Afghanistan and Pakistan to Europe and the Middle East.
Iranian officials have also accused Britain and the United States of supporting ethnic minority rebels operating within the Islamic republic's sensitive border areas, amid a worsening stand-off over Iran's nuclear ambitions.