"We will not rest until we have captured the killers," Lula said in his bi-monthly radio address.
The 74-year-old advocate for the environment and the poor was shot dead on 12 February in a settlement of landless peasants in Brazil's Amazon rain forest.
Some 2000 local people flocked to her funeral in the northern Para state last week.
The elderly nun's murder refocused national debate on the emotional issue of land distribution in the Amazon basin where ranchers, loggers and speculators frequently clash with environmentalists and landless peasants.
Fearing unrest between the two sides in the wake of Stang's slaying, Lula's government deployed troops to the region.
Two suspects have been arrested for the nun's murder: Amair Feijoli da Cunha, who is suspected of acting as a go-between for a rancher believed to have ordered a hit on Stang, and Rayfran das Neves Sales, one of two people suspected of carrying out the crime.
Dorothy Stang was shot to death
on 12 February
"With the capture of those who sent them, the government will demonstrate that there will be no impunity, that the Amazon belongs to all of us and that we will protect this territory, without wavering," Lula said.
Lula created a national park and an environmental reserve in the wake of Stang's death in Para.
The decree sets aside 8.2 million hectares in a region plagued by logging and illegal land grabs.
However, a local representative for big landowners said Stang was "responsible for her own death".
No love lost
"Dorothy Stang, she wasn't a saint, she was shameless and responsible for her own death," said Francisco Alberto de Castro, a regional director for the Agribusiness Federation of the State of Para (FAEPA) and a ranchers' union representative.
Rayfran das Neves Sales is
accused of killing Stang
Castro said "she created nothing but problems during 20 years here".
"Would people allow a Brazilian in the United States or France to incite people to invade off-limits land?" Castro asked, referring to one of the biggest causes of social tension in Brazil.
He said Stang, who had obtained Brazilian citizenship, had incited peasants to invade numerous private properties in the state, and that the municipality of Anapu had declared her "persona non grata".
Tensions in Para have flared in the past when some landowners sought to illegally expand their holdings onto publicly-owned forests.
Environmentalists and peasant rights groups have long fought a running battle with powerful landowners and land speculators.
Castro also criticised Lula's move to create the huge national park and reserve, the combined size of Austria, saying the government had done little to spur economic development in the region.
Stang is buried on the edge of the Anapu river, near an environmental agriculture project she developed in Anapu, a town 700km south of the Para state capital, Belem.