"This morning I met with Palestinian Prime Minister Rami Hamdallah in Gaza".
"This never was nor will it be up for discussion", he said in a statement distributed to reporters in Gaza.
Previous attempts at reconciliation have failed, and there are hard obstacles which still stand in the way.
Secretary of Fatah's revolutionary council, Fayez Abu Aita told Breitbart Jerusalem that he believes Hamas and Fatah are headed for true national reconciliation "in order to confront the plans of the Israeli occupation as one".
The Palestinian unity goverment, formed in 2014, has previously failed to function in Gaza because of disputes between Hamas and Fatah over its responsibilities.
Hundreds of people packed streets waving flags and cheering as Mr Hamdallah's convoy arrived in Gaza on Monday, his first such visit in two years. But it is the first expression emerging from the Trump Administration relating directly to the return of the Palestinian Authority government to Gaza and the possibility of establishing a unity government. Hamas has ruled Gaza, while Abbas' party has controlled autonomous enclaves in the Judea and Samaria area.
Hamdallah said the Authority would take over the Strip's day-to-day governance as well as "security responsibilities".
"The government began to exercise its roles in Gaza from today", Hamdallah said.More news: 22 dead, almost 40 injured in Mumbai bridge stampede
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Two weeks ago, Hamas dissolved its administrative committee running Gaza, making way for a Hamas-Fatah unity government in Gaza.
The move was facilitated by neighbouring Egypt, whose relations with Hamas have improved in recent months.
The sides instead traveled to a beachside hotel and later returned to the home of the local Fatah official in Shajaiyeh, a neighborhood near the border damaged by heavy fighting during the 2014 war with Israel. "For his part, Abbas is committed to finding a peaceful solution to the Palestinians" conflict with Israel.
Ahead of the meeting, Mr Abbas staked out a tough line on reconciliation with Hamas, warning he would not tolerate any solution short of the disarming of its Izzedin Al Qasam militia.
It also remains unclear what will happen to Hamas' 40,000 civil servants, who were hired after Abbas forced his employees in Gaza to resign after the Hamas takeover. The PA also wants Hamas to disband its armed wing.
"The reconciliation initiative was merely tactical", Ghassan Khatib, a former member of Abbas's cabinet, said in a Facebook post.
He noted that all Palestinian factions - which inked the 2011 Cairo agreement - would convene in Egypt soon.