While the PA is the only recognized quasi-government in the territories, the PLO has been the only recognized representative of Palestinian Arabs worldwide. In fact, the PLO was enshrined in that position at Oslo, as the sole representative of the "Palestinian people." The PA is effectively but not officially a subsidiary of the PLO, and the president of the PA has so far also always been the head of the PLO.
While Hamas broke with the PA and created its own de-facto terror government in Gaza, they never broke with the PLO. n fact, the PLO includes some factions who are actively engaging in terror in Gaza, such as the PFLP and DFLP.
Hamas aims to change that.
All the major Palestinian media outlets are reporting that Khaled Meshaal is planning to create its own alternative "Palestinian national authority" as a competitor to the PLO. In a speech he gave last night in Doha, saying that "there can be no reconciliation for the Palestinian people at home and abroad without a national reference," and called for "the Palestinian national authority to maintain the right of return," saying that "by the Palestine Liberation Organization preventing Hamas from entering or working on reconstruction, they no longer constitute a national reference but a deficit and an instrument of division."
This means that Hamas is no longer only challenging the PA's primacy in the territories, but now it is bidding to create a new leadership for Palestinian Arabs in other countries, including the camps in Lebanon where the PLO now has de facto political control.