While Egypt starts placing restrictions on the movement of Palestinians into its territory through the breaches in the Gaza-Egypt border fence, talks are underway between Egypt and Hamas, which is in control of the Gaza Strip, over longer-term control over the border. Egypt is also simultaneously negotiating the border issue with the administration of Palestinian President Mahmoud Abbas.
Hamas has been cooperating with Egypt over stemming the flow of Palestinians into Egypt, but wants joint control over the border with Egypt in return. Meanwhile, Abbas does not want Hamas to play any role at the border, and is refusing to enter into direct dialogue with the movement. According to Abbas, "Hamas has to end its coup in Gaza, accept all international obligations, and accept holding early elections" before any talks can begin between it and the Palestinian government.
Egypt would like Abbas's government to control the Palestinian side of the border under supervision from Israel and the EU, under a multi-sided agreement reached in 2005 (BBC).