The Truth and DignityCommission (IVD) was set up to investigate human rights violations going back six decades, following the 2011 ousting of dictator ZineElAbidineBenAli.
In February the tribunal extended its own mandate to the end of 2018, but the IVD faced an uncertain future after lawmakers voted in March to end its work.
Sihem Ben Sedrine, the body's president, said the government had granted the IVD time to wrap up after the tribunal's mandate formally ends on May 31.
"It's a gesture of appeasement which signifies that the government is committed to finishing the process. But they want the IVD to speed up a bit," Sedrine said.
"We will speed up. We don't have any interest in playing for extra time."
Sedrine estimated the IVD would need "several months" to finish its work.
Mehdi Ben Gharbia, a minister responsible for relations with constitutional bodies and civil society, said the tribunal's mandate would legally come to an end at the end of May.
The following months would allow for a handover period to ensure "persecutors are brought to justice, the victims compensated and the reports handed to the authorities," he said.
"The government cares about bringing the process to a conclusion," Gharbia added.
The tribunal has faced resistance from those within the former regime who have returned to power, while it has also struggled with internal disagreements and a lack of cooperation from state bodies.
It was tasked with investigating human rights violations between 1957, when Habib Bourguiba became president, and 2013, when the IVD was set up in the wake of the uprising.
Since March the tribunal has referred at least 32 cases of "serious violations" of human rights to Tunisian courts.
The first court case is due to open on Tuesday in the coastal town of Gabes, examining the case of Islamist Kamel Matmati who was tortured to death in October 1991.
Since the tribunal began work, it has received more than 62,000 allegations of human rights violations and interviewed close to 50,000 people.
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