(CNN) - Sen. John McCain suggested Sunday that former President Bill Clinton once again try his hand at forging peace between the Israelis and Palestinians as another day of violence lit up the sky on the border between Israel and Gaza.
Israeli Defense Forces aircraft struck targets in Gaza on Sunday, including some where they said the militant group Hamas was launching rockets. Rockets from Hamas streamed toward cities in Israel, including Tel Aviv.
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McCain spoke in an interview on CBS, saying the U.S. should be "as heavily involved as they possibly can" in the region.
"I would find someone even as high-ranking, frankly, as former President Bill Clinton to go and be the negotiator," McCain said.
"I think that it's very important that we recognize that the United States of America has got to push as hard as we can to resolve this Israeli-Palestinian issue. And so many events hinge on making that process go forward."
Clinton has hands-on experience with peace negotiation in the region, having convened leaders from Israel and the Palestinian Authority at Camp David when he was president. His wife, Secretary of State Hillary Clinton, has been in touch with her counterparts in the area since the violence escalated earlier in the week.
United Nations Secretary-General Ban Ki-moon said Sunday afternoon he would head to the region and "appeal personally for ending the violence." French Foreign Minister Laurent Fabius met with Israeli Prime Minister Benjamin Netanyahu earlier in the day, and an Israeli representative was in Egypt earlier in an attempt to negotiate a peaceful settlement.
The violence puts millions of people at risk in Israel and Gaza, and should Israeli forces staging along the border launch a ground invasion of Gaza, the violence in the densely populated Gaza Strip would increase.
President Barack Obama said Sunday that the U.S. is "fully supportive of Israel's right to defend itself from missiles landing on people's homes and workplaces and potentially killing civilians."
On CNN's "State of the Union," Rep. Dutch Ruppersberger, D-Maryland, said the situation would be akin to his state launching an attack on Washington.
"Hopefully you could take advantage of this negative situation and start talking about peace. History shows that is unlikely at this point," Ruppersberger said.
Sen. Roy Blunt, R- Missouri, said he suspected Iran was involved and said he found Obama's words on the violence "helpful."
"His statements yesterday I thought they were helpful," Blunt said. "They are in line with what the congressman and I have said here today, and I hope we're aggressively pursuing that idea that Israel has a right to protect itself. But people all over the world have a real interest in trying to stop this violence from being initiated by Hamas and Gaza."