A Special Investigation Team (SIT) formed by the Home Ministry in February 2015 to re-investigate the closed cases related to the massacre received a third extension in February this year, it said.
It has now been given time till August 2017 to complete its probe.
The SIT has told the Supreme Court that it had identified 59 cases for reinvestigation, out of the 267 closed by the Delhi Police after the massacre, it said.
The Supreme Court is hearing a public interest litigation on the functioning of the SIT, filed by Gurlad Singh Kahlon, the human rights body said.
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"It is time the government enacted a law that will make those at the helm of affairs - politicians, police and bureaucrats- accountable for dereliction of duty when they fail to prevent communal violence," Harminder Kaur, a member of Amnesty International, said.
Sanam Sutirath Wazir, from Amnesty International India, said, "The SIT has disappointed many who have struggled for justice. It has only filed four charge sheets in over two years, following a non-transparent process".
Amnesty International India launched a public campaign in 2014 on the 30th anniversary of the anti-Sikh riots to demand justice and accountability.
Since then, the campaign has gathered several supporters, including 6,00,000 in Punjab.
"Many survivors are hoping that the new government taking office in Punjab will support their demands, and help deliver the long-awaited justice," Wazir said.