The interior ministry in Gaza said it had launched a "high-level investigative committee" into the bomb attack, which was a further blow to faltering reconciliation talks between Hamas and president Mahmud Abbas's secular Fatah party.
It said a number of suspects were being questioned after the roadside bomb targeted Hamdallah's convoy shortly after he entered Gaza, leaving him uninjured but lightly wounding six guards.
It did not provide further details on the investigation Wednesday or release the identity of the suspects.
"The door is open to anyone who wants to participate in the investigation," Tawfeeq Abu Naim, the head of the Hamas security services in Gaza, said in a statement.
Hamas seized control of Gaza from Abbas's internationally recognised government more than a decade ago but agreed in October to hand power back.
Yet the deal has all but collapsed, with the two sides accusing each other of responsibility, and Tuesday's explosion further exacerbated tensions.
After the attack, Abbas said he held Hamas responsible as the de facto power in the strip, though stopping short of directly accusing the group of carrying out the bombing.
Hamas shot back, saying such rapid accusations were unhelpful before in turn pointing the finger of blame at Israel.
Other potential suspects include smaller, more radical Islamist groups that are opposed to Hamas but operate in Gaza, or a Hamas splinter group.
There has been no claim of responsibility.
Hamdallah said the attack would not end his government's commitment to continue with reconciliation and again called on Hamas to hand over all power in Gaza.
"We are talking about internal security -- the police and the civil defence," he said. "Without security there won't be a government."
Salafist suspects?
Jamal al-Fadi, a political scientist in Gaza, told AFP the aim of the attack was to "sabotage any chance for reconciliation."
He said potential suspects are those that have an interest in maintaining the split.
"It could be a group that split from Hamas for ideological reasons, such as a militant Salafi group," he said.
In October, Abu Naim, the Hamas security chief who issued Wednesday's statement, was wounded by a car bomb after leaving a mosque.
Hamas officials privately admit the assassination attempt was by Salafists, rather than Israel, and like Tuesday's attack the explosion was relatively small.
The UN envoy to the Middle East peace process, Nickolay Mladenov, condemned Tuesday's attack and called on Hamas to hand over control in Gaza to the recognised government.
Mladenov has warned of the consequences of the desperate humanitarian suffering in the strip, saying in January that Gaza "risks exploding in our face again."
Hamas has fought three wars with Israel since 2008 while the Jewish state maintains a crippling blockade of Gaza.
Hamdallah travelled to Rome Wednesday for a meeting of international donors aimed at raising funds for the United Nations' agency for Palestinian refugees, which is facing desperate shortages after the US froze tens of millions of dollars in aid.
The White House held a conference on the deteriorating humanitarian situation in Gaza on Tuesday, but no Palestinian officials attended.
They have refused to meet with President Donald Trump's administration since he broke with longstanding US policy in December by recognising Jerusalem as Israel's capital.
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