He said: "The president has given a period of only two weeks for a national dialogue ... after those two weeks we will either come to agreement or not."
Hamas, which leads the Palestinian government, and Abbas's Fatah are locked in a deadly power struggle in Gaza which has raised fears of a civil war.
Meshaal, who is based in Syria, told Reuters in an interview on Wednesday in Damascus: "There are negotiations that are going on between us and Fatah and Abu Mazen [Abbas] ...
"True that in the past there were failures in dialogue but we as Palestinians have no option but dialogue.
"There are chances for the success of the dialogue ..."
Meshaal insisted that Ismail Haniya must keep his post as prime minister.
Failed unity bid
Efforts to form a new government late last year failed after talks between Abbas and Hamas broke down over the composition and policies of a new cabinet to be made up of technocrats.
Differences between the two main Palestinian groups have widened since last year's failure to get a unity government deal and threatened to spill over into an all out war in Gaza.
"Now we are seeking the establishment of a government of national unity in which various factions and parliamentary blocs will be represented ...."
Meshaal said, he gave few other details. Several Palestinians have been killed over the past month in sporadic fighting between Hamas and Fatah fighters in Gaza.
He said US and Israeli interference was stoking tensions among Palestinian factions.
The US announced this month that it is planning to spend more than $80m to arm and train forces loyal to Abbas.
He said: "This external intervention in the internal Palestinian affairs is pouring fuel on the fire and pushing the political differences to feed conflict and internal struggle."
Meshaal said foreign sanctions and demands that any Palestinian government recognise Israel would not defeat Hamas: "These sanctions lost their effectiveness in subjugating Hamas or the Palestinian people.
"I say that this situation will not continue. Now or tomorrow sanctions must end. The bet that the sanctions would defeat Hamas will not pay off."
He said Abbas's call for early elections last month was "an illegal and illegitimate step" that would not happen.
He said the Palestinian president had no authority to dissolve the legislative council. "I think Abu Mazen knows that. If he insists on this step it means that he wants to detonate the Palestinian situation."