The Biden administration is urging Israel and Iran to refrain from doing anything to further escalate the conflict in the Middle East. This, as Iran's leaders have vowed to "punish" Israel for killing the leader of Hamas' political wing last week in Tehran.

With Israel still aggressively pursuing the total annihilation of Hamas for the Oct. 7 attack that started the war in Gaza, and Hamas, Hezbollah, and now potentially Iran fighting back, State Department officials are calling this a critical moment in the Middle East.

"Escalation is in no one's interest," State Dept. Spokesman Matthew Miller said this week.

But after the political head of Hamas, Ismail Haniyeh, was taken out in Iran last week -- allegedly by Israel -- and a top Hezbollah commander killed in Beirut, Lebanon, escalation seemed inevitable.

"Most worrying, is a coordinated, so-called 360-degree attack," Alon Pinkas, a former Israeli diplomat to the U.S., told CBS News: "Hezbollah in Lebanon. Iran from the east, the Houthis in Western Yemen from the south. Hamas in both Gaza and the West Bank. So, Israel will be encircled."

As the State Department keeps President Biden up to speed, U.S. diplomats are working with their G-7 counterparts and also with moderate Arab nations such as UAE and Egypt to try and calm tensions.

"The last thing that America wants," said Pinkas, "is a scenario in which they are dragged into the conflict."

Members of Oklahoma's congressional delegation say Israel is only doing what the United States did after 9-11.

"I'm not concerned about Israel's response," said Sen, Markwayne Mullin (R-OK) in an interview last week. "Israel has to do what they have to do to protect themselves -- they were attacked."

What does concern Senator Mullin is what he sees as the Biden administration's policy of 'appeasement' and less than full support of Israel.

"We should have no daylight between us and Israel," Mullin said. "We should be supporting them and the whole world should know: where they go, we go."

The administration has not criticized Israel for the actions taken against the Hamas and Hezbollah leaders but continues to say that a ceasefire in Gaza is the key to bringing a return of peace to the region and its inhabitants, and says it's Hamas' hands to make that happen.

Senator James Lankford says Israel is trying to give itself the best leverage to end the conflict in a way that's favorable to them.

"Israel is trying to be able to put enough pressure now on Iran, on Hamas, on Hezbollah, on the Houthis," Sen. Lankford (R-OK) said in an interview, "to be able to make it stop so they can actually negotiate a peace that will stop the cycle of violence that's happening there."