MPs on Monday agreed to review the 2004 law on management of abandoned property.
Some properties were abandoned during and after the 1994 Genocide against the Tutsi, and were later occupied by people returning from exile and survivors of the Genocide.
Tabling the new Bill, Justice Minister Tharcisse Karugarama said there are some elements which were not provided for under the current law, which government wants the new Bill to fix.
The government wants to set up a unit in the Ministry of Justice to look after the abandoned property.
Karugarama said the 2004 law established a commission in-charge of abandoned property in districts, Kigali, at the provincial and national levels, but not established at certain levels.
The Bill would make members of the commission to be full-time employees with support budget.
"Members of the old commission were public servants with other responsibilities. After five years, we realised that the commission had achieved nothing," the minister said.
A September 2009 Cabinet meeting recommended that a department be established in the Ministry of Justice to cater for the abandoned property.
"The government should identify the property so that if the owners return or are identified, they get their property in a proper manner," Karugarama said.
MP Evode Kalima said establishing the unit was long overdue since the Genocide was committed 18 years ago.
"We need to scrap it given what the minister says, but this issue requires more effort to give this Bill its required weight," Kalima said.
The lawmaker raised fears of a possibility of properties of Genocide suspects being dumped on the cheap.
MP Abbas Mukama suggested that the law must solve the tricky complications of the "many people who illegally bought abandoned property" as there are Genocide suspects who sold off before they ran away.