Bhutto said she had no doubt that members of the former Zia government were responsible for the attack.
She said there were those who had served with Zia who remained extremely powerful and saw her return to Pakistan and her pledge to restore democracy as a threat to their influence.
While acknowledging that religious extremists were likely to have been responsible for the attack itself, she said that such groups were not able to operate without logistical support from those in positions of power.
She also blamed the government of Pervez Musharraf, Pakistan's military ruler, for failing to prevent the blasts.
Bhutto said half an hour before the blasts, her entourage had received a call from the government's intelligence services warning her that they had received a bomb threat that they were taking very seriously.
She told the magazine: "They then sent a team to take down a suicide bomber that had a belt full of explosives and who was near the lorry I was in. Young people died in the explosions. They gave their lives to defend us."
With elections expected in January, Bhutto said she was worried that whenever she planned a mass rally, the government would say it was too dangerous because there could be bombers.
Al Jazeera's Sohail Rahman in Karachi said the first bomb was detonated in a car metres in front of Bhutto's armoured bus.
"Perhaps Bhutto should have listened to Musharraf and delayed her return to Pakistan until the volatile security situation was better"
ndur5, Irving, US
Send us your views
Pakistan's interior minister said he believed the attacks were the work of suicide bombers.
Kamal Hyder, Al Jazeera's correspondent in Islamabad, said on Friday: "The bomb disposal unit is saying these were planted devices. However, security aides who were close to Benazir say this was a suicide attack.
"Whoever carried out the attack, planned it very well. The attack is a signal of how violent Pakistan has become.
"Now the political parties are being lumped into religious or secular parties and that is a very dangerous divide for a place like Pakistan."
Hyder said Taliban groups had denied they were involved.
Pervez Musharraf, Pakistan's president, condemned the attack as a "conspiracy against democracy". Bhutto said Musharraf had not telephoned her after the attempt on her life.
Al Jazeera's Tim Friend in Karachi was on a motorway bridge over the scene of the attacks and described the scene shortly following the blast as "carnage".
BK Bangash, a photojournalist reporting on the procession, was about 50m from Bhutto's truck when the first bomb exploded.
"People were shouting for help, but there was no one to help them out. It smelled like blood and smoke," he said.
Groups linked to al-Qaeda, who are angered by Bhutto's support for the US "war on terror", had threatened to assassinate her.
However, speaking from Dubai, Bhutto's husband Asif Ali Zardari told the ARY television channel: "I blame government for these blasts. It is the work of the intelligence agencies."
Musharraf's government had approved the rally in Karachi and Wajid Shamsul Hasan, an adviser to Bhutto, told Al Jazeera that it was the responsibility of the government to assist in protecting her.
|Bhutto aboard the bus before the blast [AFP]|
Bhutto had earlier described herself as "emotionally overwhelmed" upon her return to Pakistan.
Joyous scenes had greeted her arrival as she stood on a truck designed to withstand a bomb attack as it edged through the throng outside the airport, ignoring police advice to keep behind its bullet proof glass.
She had earlier said she had no fears for her own safety saying that she had returned to Pakistan to do her "duty" and stand in national elections scheduled for January.
Faik Ali of the PPP rejected claims the former prime minister was wrong to return to Pakistan.