The Ampatuans allegedly ordered the massacre to stop a political rival, Esmael Mangudadatu, from running against one of its members for governor of Maguindanao.
Philippines sets deadline for massacre convictions
Leila de Lima, the justice secretary, said the government wants judgments against the Ampatuan clan, accused of perpetrating the murder of 58 people in 2009.
"The marching orders of the president [Benigno Aquino] is that during his term up to 2016, there's got to be convictions," Ms de Lima said.
She conceded that it may be impossible to convict all the suspects but hopes they can at least get the "principal accused".
The prosecution has so far completed presenting evidence and the testimonies of 130 witnesses to get on record the case against clan patriarch Andal Ampatuan Sr and other members of his family for the massacre.
Ms de Lima said the government viewed the Ampatuan massacre "as the single most important case" that needed to be satisfactorily resolved to show the public it was serious about ending a culture of impunity that is afflicting the country.
"It is a litmus test for the government," she said.
If the government fails to get convictions by 2016, "there will be a general feeling of helplessness" among the public.
The Ampatuans allegedly ordered the massacre to stop a political rival, Esmael Mangudadatu, from running against one of its members for governor of Maguindanao, a poor farming province in southern Mindanao island.
Andal Ampatuan Jr, allegedly led his clan's private army in waylaying a convoy carrying his rival's wife, relatives, lawyers and 32 journalists, and then gunning them down on a grassy hill.
Witnesses said Ampatuan Jr personally took part in the killings after his father had ordered the attack.
The Ampatuans had ruled Maguindanao for about a decade under the patronage of then-president Gloria Arroyo, who had used the clan's militia as a buffer against Muslim separatist rebels in the region.
The Ampatuan patriarch, two sons and several family members are among those in detention while being tried in the emotionally-charged case.
But the Ampatuans remain influential. They have a battery of highly paid lawyers representing them and they are opposing every move by the prosecution, Ms de Lima said.
There are 72 clan members - not accused in the case - who are also running as candidates in this month's local elections, including so-called "good Ampatuans" under the political party of Mr Aquino.
Ms de Lima said at least 12 witnesses are under state protection.
At least three witnesses have been killed since 2010, including a former Ampatuan family employee whose dismembered remains were found stuffed into a sack last year.