In an interview for Voice of Palestine radio, Al-Ahmad said that the issue of the government and ministers' work remains standing, and that new problems have emerged, despite the presence of the Egyptian security delegation in the Gaza Strip.
Several people were lightly wounded in the incident, according to Israeli daily Haaretz.
Hamdallah was reportedly visiting Gaza, along with Palestinian intelligence chief Majid Faraj, to open a water treatment plant that the Palestinian Authority helped finance.
Three of the vehicles in his convoy were damaged, their windows blown out.
"We condemn the crime of targeting the convoy of Dr. Rami Hamdallah", said a Hamas statement posted on Twitter.
"The prime minister was unhurt in the attack", Wafa said.
Mr Hamdallah was unharmed, but there are reports of some injuries.
Hamas won parliamentary elections in the occupied territories the previous year, and reinforced its power in Gaza after ousting Fatah from the enclave.
Regarding the convening of the national council, Al-Ahmad said that Hamas was not invited to attend because it would be held with its current formation and Hamas remains outside this shape due to the continued division.
He said that despite the attack he remained committed to Palestinian unity and would continue to come to Gaza.
Hamas has controlled Gaza since seizing it from the West Bank-based Palestinian Authority in 2007.
He was also met with senior Hamas officials to discuss reconciliation talks between Hamas and the PA.