Opponents of the amendment, which has been in the works for some time, claim that it would allow the government to arbitrarily confiscate land from owners.
"There is already a history that it [the law] would be abused should such a change be done," Henry Nickson Ogwal, director of Action Aid Uganda told RFI.
For him the bill in its current form goes against the constitution, which says that there must be "prior, adequate, fair compensation before the land is taken from anyone".
Ogwal is not the only one who thinks that.
Several opposition MPs have been putting pressure on the ruling National Resistance Movement (NRM) to drop the amendment bill.
On Wednesday, after a heated meeting at the State House, they received a temporary reprieve.
Museveni agreed to set up a special committee to look into the Land Acquisitions Act, and then deliver its conclusions in the coming weeks.
"I see a strong indication that this law will be struck down," reckons Ogwal, without denying the need for development.
"We all agree that there is need for a land acquisition law," he says. "But the government must settle the land it may require legally and constitutionally."
Fears over potential land grabs have come to the fore particularly in the northern district of Amuru.
"The government has always wanted that land for the last 10 years, even without the amendment," the area's MP, Akello Lucy, told RFI.
However, she does think that the amendment "would actually boost the government in ensuring that they don’t struggle with the people when they want to acquire land" and allow it to sell it off to the highest bidder.
In Amuru's case that happens to be major investment company Madhvani Group, which wants to build a sugar factory on the 10,000-hectare plot.
It has the government's approval and the government has been trying to get locals' agreement. Except that efforts to conduct a survey of the land have been met with resistance.
Last week Lands Minister Betty Amongi was greeted by angry protesters, who stripped naked in protest at the plan.
Images of people being teargassed by police were later published.
Contacted by RFI, Minister Amongi said the survey was going according to plan and had been very successful.
"Yes, she can call it successful, but legally it is not successful because the use of force is not called for really," asserts Lucy.
"If it was the will of the people, I am not sure they would be needing all that security, actually the security would be the people themselves and not the army and the police that they’ve deployed."
Lucy maintains that the people of Amuru are not averse to investment, what they are unhappy about is the government's approach.
"Forcing those who are not willing to give up their land and then intimidating them. That is why there has been really serious resistance."
Contentious land history
Land is a sensitive issue in Uganda, particularly in the north where there have been long-running disputes over who actually owns what.
"There is a history in this country in the past, when the government had taken the land of citizens for different purposes, including for development projects but without paying them," explains Ogwal.
In northern Uganda land disputes have often been triggered by former refugees returning from displacement camps seeking access to their land, some of which the government had already sold to the Madhvani Group.
"The government has set the problem it is solving as being failure of government projects to be implemented in time," says Ogwal.
"Yet it is corruption and inefficiency that is slowing down these projects," he says. "Amending the constitution is the wrong solution."