Will Egypt's new president end the Gaza blockade?
President Mursi has had very little time to deal with anything except his own delicate position and the power sharing he must work out with the military.
But Hamas seems fairly confident that eventually, Mursi will lift the blockade that has prevented most arms from flowing into Gaza.
The Gazan Islamists long complained that his predecessor Hosni Mubarak, ousted from power last year in a popular revolt, sided not just with Israel, but also with their political rival -- Palestinian Authority President Mahmoud Abbas's Fatah movement.
So far, Hamas has seen little sign of a policy shift since Mursi took office and diplomats said the Egyptian leader had so many domestic problems that he could ill-afford to dedicate much time to re-tooling Cairo's relations with the Palestinians.
However, Ismail Haniyeh, the head of Hamas's Gaza government, told worshipers in a mosque that change was coming.
"We are confident that Egypt, the revolution led by Mursi, will never provide cover for any new aggression or war on Gaza," he said. "We are confident that Egypt, the revolution led by Mursi, will not take any part in blocking Gaza," he added.
Israel launched a military offensive against Gaza in late 2008 in an effort to end repeated rocket attacks from Hamas, which refuses to recognize Israel's right to exist. Some 1,400 Palestinians and 13 Israelis died in the three-week war.
Low level violence continues and Israel still imposes a rigid trade blockade on Gaza, arguing that it is needed to prevent weapons of arms-making materials into the enclave.
Politicians in Israel have expressed alarm in private over the election of Mursi and fear that their country's historical peace treaty with Egypt could be eroded over time.
It would be disastrous for Israel if the Egyptians were to allow the free flow of traffic through its border with Gaza. It would also be the beginning of the end of the peace treaty. So far, Mursi has moved slowly in domestic affairs and one would expect that caution to continue in foreign affairs as well. This means he may not move to open the border immediately, nor will he seek to destroy the treaty with Israel anytime soon.
But both eventualities will probably come true within the next year.