The explosion occurred shortly after the convoy entered Gaza.
The Washington delegation entrusted with coming up with a peace solution to the Palestinian-Israeli conflict called for the meeting in order to find solutions for the humanitarian crisis in Gaza.
He underscored Jordan's historical commitment to defending the Palestinian issue at all regional and worldwide arenas.
Palestinian MP and dismissed Fatah leader Mohammed Dahlan called on Tuesday for setting up a national team to investigate the explosion that hit the convoy of the Palestinian Authority Prime Minister Rami Hamdallah in Gaza, Shehab.ps reported.
"The situation in Gaza must be solved for humanitarian reasons and for ensuring the security of Egypt and Israel", the White House said in a statement Wednesday.
A minister in Hamdallah's government told Voice of Palestine radio that Hamas informed them that there were two 15-kilogramme (33-pound) bombs, the second of which was planted 30 metres away, but failed to explode.
White House officials presented specific project ideas to aid the Palestinians in Gaza, developed with the National Security Council staff and the State Department, proposals that may be addressed at an upcoming conference in Brussels, home of the EU.
A number of officials have been travelling to the enclave in recent months to discuss reconciliation. Hamas has been controlling Gaza since 2007 after ousting the forces loyal to Abbas.
No group has claimed responsibility for the bombing, which Hamdallah describes as an "assassination attempt".
Other potential suspects include smaller, more radical groups that are opposed to Hamas, but operate in Gaza, or a Hamas splinter group.
For his part, Palestinian ambassador to Cairo Diab Allouh denied that Hamas was ever charged with the incident, in a response to allegations made by some media outlets.
Under the deal, Hamas should fully hand over its power in Gaza to Hamdallah's Ramallah-based consensus government in December.
"We are talking about internal security - the police and the civil defence", he said.