Speaking at a joint press conference with his Jordanian and Egyptian counterparts in Cairo, Al-Maliki said Egypt was fulfilling its role as a mediator between the group and the Palestinian Authority.
"It is not new or controversial for Egypt to do its part and fulfill its mandate in these negotiations ... it must communicate with Hamas in order for the group to mesh with the overall Arab stance," Al-Maliki said, following a meeting between the three parties to discuss the Israeli-Palestinian peace process.
For much of the last decade, Egypt had joined Israel in enforcing a land, sea and air blockade of the Gaza Strip, a move to punish Hamas and its armed wing, which seized the territory in 2007 and has controlled it since.
In recent months, however, Egypt hosted a number of Hamas members including its leader Ismail Haniyeh in a series of meetings that showed improved ties between the country and the group.
After the last round of meetings in Cairo, Hamas cleared land on its side of the border, creating a buffer zone with watchtowers, cameras and barbed-wire fences in a concession to security-conscious Egypt, which has battled an Islamic State-led insurgency in its Sinai Peninsula that has killed hundreds of soldiers and police officers since 2013.
An Islamist militant killed a Hamas security official on the Gaza Strip's border with Egypt on Thursday, in what was described as the first suicide bombing against Hamas.Al-Maliki called on Hamas to relinquish control of the Gaza-Strip in order to pave the way for legislative and presidential elections.