Khaled Meshaal was speaking in the Tunisian capital days after Abbas threatened to break off a unity agreement with Hamas, saying it was not allowing the government to operate in the Gaza Strip.
"There is a national unity government; talk of a parallel government is totally against reality," Meshaal said after meeting Tunisian President Moncef Marzouki.
He said government ministries were still "operating normally" in Gaza even if the "government is absent from" the coastal enclave and urged the cabinet to be present.
In April, Hamas agreed to work with its rivals in Abbas's Fatah movement to form an interim consensus government of technocrats which would work towards long-delayed national elections.
The deal sought to end years of bitter and sometimes bloody rivalry between Hamas and Fatah, which dominates the West Bank-based Palestinian Authority.
The new cabinet took office on June 2, with Gaza's Hamas government officially stepping down the same day.
But last week Abbas accused Hamas of running a parallel administration in Gaza.
"The national consensus government cannot do anything on the ground," he charged.
On Monday Hamas accused Abbas of trying to sabotage the unity deal.
The spat erupted after an open-ended ceasefire took effect in Gaza on August 26, ending a major 50-day conflict between Hamas and Israel.
Talks between the two sides are due to resume in Egypt later this month to consolidate the truce.
Exiled Hamas deputy leader Mussa Abu Marzuq yesterday said the group could be forced to negotiate directly with Israel -- something it has never done before.
"Direct negotiations with the Israeli occupier is not on the agenda of Hamas; if negotiations are necessary they must be indirect," he said.