( 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 .
Abdullah al-Thinni is stepping down after he and his family were attacked . The attack took place in the town of Qusayr near Damascus on Saturday night. A resident in al-Thinni 's Tripoli neighborhood told CNN a militia was responsible .