Secretary of State John Kerry arrives in Cairo, Egypt, July 21, 2014. (Charles Dharapak/AP Photo)

CAIRO, EGYPT - As fighting in between neighboring Israel and Gaza rages on, Secretary of State John Kerry arrived here with a mission to try to stop the bloodshed - but his first task is to get the many stakeholders in the region to agree on what would even constitute a ceasefire.

Kerry came to Cairo because Egypt has been a key mediator between Israel and Hamas, the governing body of Gaza, which the U.S. and Israel consider a terrorist group. Egypt also released a proposal for an immediate ceasefire without conditions on either side, which Israel accepted but Hamas rejected.

Kerry is here now, rather than earlier in the conflict, partly because of the mounting civilian casualties on both sides of the Israel/Gaza border, but especially since Israel began its ground invasion of Gaza on Thursday.

"We are deeply concerned about the consequences of Israel's appropriate and legitimate effort to defend itself," Kerry said just before a meeting with United Nations Secretary General Ban Ki-Moon late Monday night.

"But always in any kind of conflict, there is a concern about civilians," he added.

Ban was more vehement in laying blame on the Israelis, also urging them to let up on trade and travel restrictions in Gaza so that Hamas, he said, won't have to resort to violence.

"I understand that Israel has to respond militarily, but there is a proportionality and most of the death toll is Palestinian people," Ban said.

Sunday was the bloodiest day so far in the Israel/Gaza crisis, with the Gaza Health Ministry reporting hundreds of deaths, many of which the U.N. said were civilians, and the Israel Defense Forces announcing the highest number of Israeli soldiers killed in the conflict thus far.

Earlier today as Kerry was en route to Cairo, a senior State Department official said that the United States had very few expectations for the next few days and that the primary objective was about getting the various players in the ceasefire negotiations on the same page, including Egypt, Qatar and Turkey, where Hamas' exiled leadership is based, and Israel.

"It's very complicated and it may very well take several days to get this done," the official said. Hamas has previously called for preconditions for a ceasefire agreement, including the release of prisoners in Israel and a re-opening of Israel-Gaza border crossings.

Kerry is scheduled to meet with Egyptian officials on Tuesday, including President Abdel Fattah al-Sisi, Foreign Minister Sameh Shoukry, and Arab League Secretary General Nabil Elaraby.

A second official said Kerry was best equipped to meet with parties on the ground at this time, versus continuing to communicate via phone, because the United States is the only stakeholder that shares good relationships with all the governments involved, except Hamas.

"It's really only the Secretary of State who can come in and have close relationships with all the parties and who can get them all on the same page," the official said.

Kerry is expected to stay in Cairo through Wednesday morning, but officials said he would make changes to his schedule, and add additional stops in the region, as warranted.