Abbas had previously said the Hamas was responsible as it controls security in the Palestinian enclave, but Monday evening said they were "behind the attack."
Hamdallah was uninjured in the March 13 attack, which saw a roadside bomb explode as his convoy entered Gaza in what Palestinian officials have called an assassination attempt.
Six of his security guards were lightly hurt.
Hamas calls for new Palestinian uprising
Speaking to Palestinian leaders in the West Bank city of Ramallah, Abbas said if the attack had succeeded it would have "opened the way for a bloody civil war."
He said the incident would "not be allowed to pass" and announced he would take unspecified "national, legal and financial measures."
Hamas condemned what it called Abbas's "provocative positions," saying its security services were still investigating the explosion.
The Islamists and Abbas's secular party Fatah have been at odds since 2007 when Hamas seized control of Gaza in a near civil war.
Abbas controls the internationally-recognised Palestinian government, based in the occupied West Bank which Hamdallah leads.
Israel says no talks with Palestinian govt that includes armed Hamas
Abbas has previously taken a series of measures, including reducing electricity payments for Gaza's two million residents, in what analysts said was an attempt to punish Hamas.
Hamas and Fatah agreed a reconciliation agreement in October but it has collapsed.
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