He said a powerful country such as the U.S. had no right to impose sanctions on other countries.
Local police official Wajeet Khan said the blast happened Sunday in the village of Sanjdi, about 30 miles east of Quetta.
Amid the ongoing US-Iran dispute, Abadi was set to visit Iran to discuss economic relations.
In July 2017, the two countries signed an agreement to promote interaction and share experiences in the fight against terrorism and extremism, work together to ensure border security, and provide each other with training and logistical, technical and military support.
Al-Abadi's remarks came at a news conference in the capital, Baghdad, on Monday, the same day that it was reported that Iran cancelled an upcoming visit by him.
Washington says the renewed sanctions are meant to pressure Tehran to halt its alleged support for worldwide terrorism, its military activity in the Middle East and its ballistic missile programmes.
Tehran has maintained close ties to Baghdad's government since the 2003 US-led invasion toppled former dictator Saddam Hussein, Tehran's archenemy.
"Iran's strategic objective in Iraq doesn't change, they want an Iraqi government that is mindful of the fact that they have to walk a tight rope in balancing multiple factions, the Kurds, the Sunnis".
The anti-Iran sanctions are set to be followed by a second wave on November 5, targeting Tehran's oil and gas sector.
The US has warned that it will restrict trade with any country which ignores the sanctions.
Former Iranian interior minister, Abdullah Ramadan Zadeh, called on Friday on his country not to oppose dividing Iraq ahead of the imposition of U.S. sanctions on the Islamic Republic.