Israel has largely refused to let foreign diplomats pass through its checkpoints into Gaza since it tightened its blockade on the territory after Hamas Islamists seized it in 2007.
The official, speaking on condition of anonymity, said Lieberman extended the invitation to Italian Foreign Minister Franco Frattini during a visit to Italy so that top European diplomats could see there was no humanitarian crisis in the coastal enclave.
The delegation could come within weeks but would not meet Hamas officials, the Israeli official added.
Prime Minister Benjamin Netanyahu, facing mounting international pressure, announced on Sunday that Israel would ease its embargo to let in all goods except for arms and materials that could be used for military purposes, such as cement and steel.
The blockade has been criticized as collective punishment of 1.5 million Palestinians in a bid to weaken Hamas, which refuses to meet Western demands that they recognise Israel and renounce violence.
Israel came under strong pressure to soften the policy after an international outcry earlier this month when its commandos killed nine pro-Palestinian activists on May 31 during a raid on a convoy of Gaza-bound aid ships. Egypt opened its border with Gaza in the wake of the incident.
Lieberman asked Frattini to lead the trip, which will also include a visit to Israeli towns along the Gaza border that have been frequent targets of Palestinian rocket fire, because of Italy's close relationship with Israel, the official said.
