The draft, backed by Britain, France and the United States, calls for the "full cooperation of Lebanese authorities" with an investigation commission to be set up by UN Secretary-General Kofi Annan.
It calls al-Hariri's killing a "terrorist act" and authorises the commission to collect any additional evidence and information in Lebanon.
A UN fact-finding report last week accused neighbouring Syria of creating an unstable environment that led to the 14 February killing of al-Hariri.
Among other charges, the report said Syrian President Bashar al-Asad had threatened physical harm against al-Hariri over his opposition to Damascus, and it called for an international investigation.
It also said the Lebanese investigation into the blast that killed al-Hariri had been flawed. Damascus says it had nothing to do with al-Hariri’s killing and accuses its political opponents of opportunism.
Striking a balance
Speaking to Aljazeera from Cairo, Salah Amir, a professor of international law at Cairo University, said that the draft resolution should strike a balance between international expectations and Lebanon's sovereignty.
Amir said that an international investigation does not necessarily mean an international trial: When the crime is solved, suspects will be tried before Lebanese courts and not necessarily before an international court.
"The proposed committee will get its authority from the power of the resolution of the UN Security Council," he added.