Abbas's Fatah movement was defeated in five days of fighting earlier this month, leaving Hamas in control of Gaza and Fatah in charge of the West Bank.
While Hamas has offered the defeated Fatah fighters an amnesty, Fatah forces have disappeared from Gaza streets.
Karni, the main cargo passage between Gaza and Israel, has been closed since the Hamas takeover.
The wheat was passed over the wall to the Palestinian side through a chute ordinarily used to transfer massive amounts of gravel, a system that required no opening of the terminal.
While the co-ordination of the shipment was done with Abbas' forces and the UN, Hamas security officials were guarding the perimeter of the terminal while the operation was under way.
Shlomo Dror, an Israeli military spokesman, said that previously aid has moved in trucks into Gaza through smaller crossings that are less of a security risk.
On Thursday, the number of trucks that passed through the crossing topped 100 for the first time since the Hamas takeover in mid-June, double the daily number needed to stave off food shortages, Dror said.
He said the pattern of co-operation with Abbas' men and international agencies "is something we intend to preserve. Our model is to strengthen Abu Mazen [Abbas], not Hamas".