Donald Trump's incoming Middle East envoy has met the prime ministers of Qatar and Israel to kick-start the U.S. president-elect's diplomatic push to reach a Gaza ceasfire and hostage release deal before he takes office on Jan. 20, a source briefed on the talks told Reuters on Wednesday. Steve Witkoff, the incoming envoy, traveled to Qatar and Israel in late November, the source said. The meetings signal that the Gulf state of Qatar has resumed its role as a key mediator after suspending that role last month, the source said, adding that negotiators from militant group Hamas would likely return to the Qatari capital Doha to facilitate a fresh round of talks soon.