No group has said it carried out the attack, which injured six security guards.
Majed Faraj, the Palestinian Authority intelligence chief, was part of the convoy.
Hamdallah said that his government is ready to meet all needs in the Gaza Strip as it is doing in the West Bank. "It was a well planned attempt", he said.
Hamdallah reportedly called the attack "well prepared and the bomb was buried two meters [6 feet] into the ground", according to Wafa.
Palestinian president Mahmoud Abbas of the ruling Fatah party termed it as "terrorist attack" while blaming the ruling party of Gaza Hamas.
The PA has also accused Hamas of refusing to permit Palestinian civil servants to return to the jobs they held before the terror group's violent takeover of the Gaza Strip in the summer of 2007. It promised an "urgent" investigation.
"Egypt will keep exerting efforts to achieve reconciliation and empower the Palestinians run their affairs according to a unified vision to achieve the aspirations of the Palestinian people", it said. A second device failed to explode, the official said.
Footage of the area shortly after the blast indicated that the bomb was small but it appeared timed to hit Mr Hamdallah's convoy.
Hamas and Fatah, the two main Palestinian political parties, signed a reconciliation agreement in October 2017, ending a decade of division that saw two parallel governments operating in Gaza and the West Bank, respectively.
While Hamas did hand over control of Gaza's borders to the PA, it maintains full control of the rest of Gaza, with its police force and armed wing still operating throughout the territory.
The World Bank, European Union and other European governments have paid almost $75 million in funding. "Without security, there won't be a government or an authority".
A White House "brainstorming session" to be held Tuesday on alleviating the acute humanitarian situation in the Gaza Strip will see Israeli officials sit alongside those from key Arab states including Saudi Arabia and the United Arab Emirates.
The Palestinians were enraged by President Donald Trump's decision to break with longstanding USA policy by recognising Jerusalem as Israel's capital and have refused to meet with his peace envoys since.
It is clear to the European Union that "those who work to exacerbate divisions through violence are working against the interest of the people of Gaza and of all Palestinians", she said.