Mr. Mitchell would head to the Middle East as soon as possible to shore up the fragile truce between Israel and Hamas in Gaza.
Israel must re-open the border crossing into the Gaza Strip "to allow the flow of aid and commerce," Mr. Obama said.
"Hamas must end its rocket fire... The United States and our partners will support a credible anti-smuggling and interdiction regime so that Hamas cannot re-arm," he added.
But Hamas spokesman Osama Hamdan told al-Jazeera television that Mr. Obama would fail in the Middle East unless he changed his position.