"[President Obama] has to express those concerns and say, obviously, we want this change to not just be democratic but also supportive of stability and also protecting minorities and human rights in Egypt," Levin said during an appearance on NBC's "Meet the Press."
"If Egypt takes some real responsibility for making the cease-fire work, we'll stop those missiles from going through the tunnels in Gaza, and they seem to be moving in that direction," Levin said. "That can make a real difference in terms of what's going on in Gaza and their attacks on Israel, which have been the cause of the whole thing."
Levin also said the administration should focus its attention on Iran, which he sees as the true destabilizing force in the region.
"Iran's support of Hamas, Hezbollah, Syria, and the way that has been filtered into weaponry that goes through Egypt, into Gaza, if that can be stopped, by Egypt, and if Iran can get a message that the missiles are not going to succeed against Israel because [of] their defenses against short-range missiles, in this case, with the Iron Dome system, but also with the Patriot system against possible Iranian long-range missiles, is going to take leverage away from Iran," Levin said. "Keep pulling the world together against Iran. That's the source of the problem."
During his interview, Levin also touched on domestic issues, arguing the "we all ought to be worried" about the effect going over the fiscal cliff would have on the economy and security of the nation.
"Whether you're worried about the regulation of our food safety, whether you're worried about our borders being secure, whether we're worried about the FBI being supported, it's all affected by sequestration," Levin said.
The Michigan lawmaker said his colleagues in the GOP must "move away from the ideologically rigid position, which has been the Grover Norquist pledge, which most of them signed, that they will not go for additional revenues."
"You've got to raise additional revenues, including tax rates on the wealthy," Levin said. "They have to go up."