(CNN) -- Libya's newly appointed Prime Minister Abdullah al-Thinni stepped down from his post on Sunday after an attack on him and his family.
The General National Congress, the country's interim parliament, appointed al-Thinni Tuesday as interim prime minister and gave him a week to form a new cabinet.
In a letter to the GNC posted on the government's website, al-Thinni said he and his family were the victims of a "cowardly attack" on Saturday night, a "shooting that terrified people in a residential area and endangered the lives of some."
"I do not accept a single drop of Libyan blood be shed because of me and I do not accept to be a reason for fighting among Libyans because of this position," al-Thinni said. "Therefore I apologize for not accepting my designation as interim prime minister."
Al-Thinni said he and members of the cabinet will continue their work as a caretaker government until a new prime minister is chosen by the GNC.
Before his appointment on Tuesday, al-Thinni had taken over the cabinet as acting prime minister after his predecessor, Ali Zeidan, was voted out by the GNC last month.
Zeidan, who was briefly kidnapped by a militia while in office, fled to Germany after his ouster because of security threats.
There were no injuries reported in the attack on al-Thinni and his family, and no details about the incident were released.
A resident in the neighborhood told CNN that al-Thinni was with his family when his convoy came under attack by a militia close to the area where he lives in Tripoli. After they escaped the attack and entered the neighborhood close to Tripoli's airport road, heavy gunfire erupted in the area.
There have been increased concerns about the worsening security situation in Libya and the country's rocky transition to democracy after the overthrow of Moammar Gadhafi in 2011.
The government has so far been unable to build an army and a police force to rein in the hundreds of militia groups with competing interests, ideologies and agendas who continue to destabilize the North African nation.
Officials have frequently been targeted and intimidated by the different militia groups.
While serving as defense minister, al-Thinni's son was kidnapped in Tripoli last September and released earlier this year.