The seven were detained more than four years ago and found guilty of terrorist activities with the organisation that later formed the backbone of the Islamic State group.
“Death sentences by hanging were carried out Wednesday against seven terrorists from Egypt, Tunisia, Libya, Sudan, Palestine, Syria and Jordan in Nasiriyah prison,” said Dakhel Radhi.
Radhi is a member of the provincial council of Dhiqar, the southern Iraqi province of which Nasiriyah is the capital.
An official in the Nasiriyah prison administration speaking on condition of anonymity said the seven had all been jailed for more than four years but could not provide further details.
He said around 60 other convicts from Yemen, Saudi Arabia, Syria, Egypt, Libya and Algeria were still held in Nasiriyah prison on similar charges.
He did not say how many of them had been sentenced to death.
On August 21, Iraq hanged 36 men convicted over the 2014 massacre by Sunni jihadists and allied militants of up to 1,7000 military recruits.
Rights group Amnesty International said at the time that the hangings brought to at least 81 the number of executions carried out by the Iraqi state this year.
Amnesty and other rights organisations had also criticised the hangings as resulting from botched trials.