In particular, the government has been dragging its heels in setting up a truth and reconciliation commission.
The government also has failed to publish several reports into suspected and alleged crimes and human rights abuses, Amnesty International said in its "Time to Face the Past" report on the conflict.
Aceh, which lies at the northern tip of Sumatra and a short distance across the Strait of Malacca to Malaysia, is one of Indonesia's poorest regions although rich in natural resources.
The majority of the province's 4.5 million people are Muslim and Aceh hits international headlines "either due to its strict implementation of Shariah-based laws whose provisions often violate international human rights standards or in the context of the Asian natural disaster of December 2004 which left over 260,000 people dead or missing," the 76-page report said.
"Despite sporadic violent incidents since August 2005, especially in the context of local elections, Aceh has enjoyed relative peace over the last seven years."
Nearly 30 years of fighting formally ended in August 2005 when the Indonesian government and the armed independence group Free Aceh Movement -- now disbanded -- signed a memorandum of understanding.
The peace accord was arranged by the Crisis Management Initiative, based in Helsinki and headed by former Finnish President Martti Ahtisaari.
The government twice designated Aceh a "military operations zone" and Amnesty International estimates 10,000-30,000 people, mostly civilians, were killed in the conflict.
Crimes committed by government forces during the conflict may amount to war crimes and crimes against humanity, Amnesty International said.
Amnesty International called for these and other crimes including torture, extrajudicial execution and enforced disappearance must be investigated and fair trials in accordance "with international law and standards without recourse to the death penalty."
Victims and their relatives "have long been denied truth, justice and reparation in violation of Indonesia's obligation under international law. They are still waiting for local and the government to acknowledge and remedy what happened to them and their loved ones during the conflict."
The report is based on Amnesty International's visits to Aceh in May when it spoke with non-governmental organizations, community organizations, lawyers, parliamentarians, local government officials, journalists and more than 30 victims and their representatives.
Victims and their relatives said they welcome the peace process and the improved security situation in Aceh.
But "they don't understand why commitments contained in the 2005 agreement to set up a Human Rights Court for Aceh and an Aceh Truth and Reconciliation Commission have yet to be implemented."
"Family members still do not know what has happened to disappeared loved ones and are struggling to get by, while those responsible walk free," said Isabelle Arradon, Amnesty International's deputy Asia Pacific director.
"The situation is breeding resentment that could sow the seeds of a future return to violence," she said.
Amnesty International also said it wants representatives of the former Free Aceh Movement, including the Aceh governor and representatives of the Aceh Party, to acknowledge publicly that human rights violations and abuses, including possible war crimes and crimes against humanity, were committed during the Aceh conflict and commit publicly that there will be no impunity for crimes under international law.
Amnesty International said it wants former rebels to make "a formal and public apology to all victims of human rights abuses committed by (them) during the Aceh conflict."
The government hasn't responded to Amnesty International's report or the group's claims, the BBC reported.
Tensions often run high in Aceh over use of the officially banned separatist flag.
Earlier this month around 3,000 people demonstrated with a giant flag at the main mosque in Aceh's capital Banda Aceh and then marched to the provincial Parliament building, a report by the Jakarta Post said.
The red flag, with a white crescent and star, was waved amid cheering of "Allah Akbar," or God is great, and "Long live Aceh."
The Aceh Legislative Council passed a bylaw allowing use of the flag and central government in Jakarta is reviewing the situation, the Post report said.
President Susilo Bambang Yudhoyono said the move could be a setback to a 2005 peace deal.
"We have evaluated their bylaw," Home Affairs Minister Gamawan Fauzi said. "We will soon convey the results to the local government."