Meshaal's comments came as Israel approved a list of more than 250 Palestinian prisoners to be released as part of a "goodwill gesture" towards Fatah leader Abbas.
He also played down a meeting between Abbas and Ehud Olmert, the Israeli prime minister, and said Hamas would never give its blessing to any deal that does not respect the rights of the Palestinians.
Fatah has accused Meshaal of orchestrating Hamas's takeover of Gaza last month.
The takeover and subsequent sacking of Hamas's Ismail Haniya as prime minister have intensified tensions between the two main Palestinian factions.
Meshaal told Al Jazeera that the emergency government appointed by Abbas was "illegitimate and illegal".
However, he said he "supported dialogue" with the president.
On Monday, the exiled leader told a gathering of Muslim clerics in the Qatari capital Doha that "we want a Palestinian dialogue under Arab-Islamic auspices".
But, he said, Bush's actions showed that he rejected inter-Palestinian dialogue.