But former U.S., Palestinian and Israeli officials said that options are extremely limited -- and that Washington must be careful to not set expectations too high or risk making the situation worse.
Secretary of State John Kerry said on Tuesday that he is planning a trip to the region "soon," although officials said the date and location have not yet been set.
"We're working on trying to calm things down," Kerry said at Harvard University. "And I will go there soon at some point, appropriately, and try to work to reengage and see if we can't move that away from this precipice."
Although the Obama administration has been careful not to place blame on any party for the latest escalation of violence, the officials said Kerry is particularly concerned about statements by Palestinian officials inciting their people to violence.
"This violence and any incitement to violence has got to stop," Kerry said at a separate event. "The situation is simply too volatile, too dangerous. And it is not going to lead to the outcome that people want, which is to have a peaceful resolution of the differences."
He added, "We continue to stress the importance of all persons of responsibility to condemn the violence on either side and to avoid provocative statements."
U.S. officials said Kerry is concerned about heavy-handed treatment of Palestinian rock throwers by Israeli security forces, particularly the use of live ammunition against young protesters.
And, in his remarks at Harvard, Kerry pointed to Israeli settlement construction.
"There's been a massive increase in settlements over the course of the last years," he said. "Now you have this violence because there's a frustration that is growing, and a frustration among Israelis who don't see any movement."
The U.S. officials said Kerry hopes to meet separately with Israeli Prime Minister Benjamin Netanyahu and Palestinian Authority President Mahmoud Abbas when he travels to the region.
A challenge to the two-state solution
"He is worried about the violence itself, but is generally concerned about where the whole two-state solution is going," a senior official said.
But former officials and experts worry that a visit by Kerry so early in the outbreak of violence could risk damaging the fragile situation even further by pushing too hard for a solution. And neither Netanyahu nor Abbas has particularly good relations with the Obama administration after years of fruitless efforts at diplomacy and, in the case of Israel, sharp disagreements over the recent Iran nuclear deal.
Stanching the violence is a tall task for the United States, which must seem concerned and involved in efforts to restore peace but can't overplay its hand. Another failed mediation effort could erode confidence in the United States even more and serve as a black eye for Kerry and President Barack Obama. Kerry held intensive talks with the parties and made repeated visits to the region in a bid for a peace deal that fell apart in spring 2014.
"In the immediate term, I don't think there is much space for high diplomacy," said Ghaith al-Omari, a senior fellow at The Washington Institute for Near East Policy and a former Palestinian Authority official.
But he said the United States can play a role in encouraging both sides separately to take productive steps. For the Israelis, that would include making improvements in quality of life for Palestinians, and on the other side, the Palestinian Authority should tone down its rhetoric and focus on a positive message, he said.
Al-Omari's sentiment was echoed by Dan Arbell, a senior fellow at the Brookings Institution and a former senior member of Israel's foreign service.
"Kerry's efforts (at a peace deal) last year failed. While he'll be listened to and he'd be used perhaps as a conduit to convey messages from one side to another, I'm pretty skeptical about what he can achieve at this point in time," Arbell said, adding the violence needs to subside before anything more substantive can be done.
"Kerry can put pressure on (Abbas) at this point and ask the Israelis to look at concrete ways of offering the Palestinians, once the violence is over, a political horizon, or that negotiations can be resumed," Arbell said.
Kerry would need to walk tightrope
White House Press Secretary Josh Earnest, in a briefing with reporters Wednesday, seemed to acknowledge to some extent the limitations the United States faces.
"Ultimately, ending this conflict will require both sides making some difficult decisions, some decisions that will require them to exercise some significant political courage," said Earnest, who noted U.S. officials were in touch with both sides. "But ultimately, what the United States can do is to try to facilitate those conversations, to try to be supportive of that process."
Elliott Abrams of the Council on Foreign Relations and a former Middle East adviser to President George W. Bush, said two major factors complicate Kerry's efforts, particularly if he were to try yet another broad push for a peace deal.
He cannot appear to be rewarding terrorism -- "if the thing that gets you back at the table is killing Israelis, that's a very unhelpful lesson to teach" -- and with Abbas aging and in a weakened position, Palestinians are facing a succession battle, Abrams said.
Abrams also faulted Kerry for his comments linking the current violence to settlement expansion, which the former Bush official said had not occurred to the extent the secretary of state maintained: "To say what he said at Harvard this week, that the massive expansion of settlements is the cause of it, I think it's actually false and it's going to make it impossible for the Israelis to work closely with him."
Instead of trying to secure a peace deal, Kerry should focus on improving conditions on the ground, Abrams recommended.
"He's taking a risk, because if he goes and then violence continues or even increases, that will be a defeat for him, obviously. I think he needs to be very careful about his rhetoric," Abrams said.
Difficulty in calming the situation
Former State Department Middle East negotiator Aaron David Miller gave some cause for hope that the United States could be helpful, noting that the United States had assisted in tamping down Israeli-Palestinian violence last year -- bringing Netanyahu and Jordan's King Abdullah together -- even if Kerry at this moment cannot produce significant "deliverables" on the ground.
Miller stressed that Obama has only a little more than a year left in his presidency and the Iran deal is his top regional priority.
"He does not want to pick another fight with the Israelis, and that fact (is) that Netanyahu isn't looking for a fight with Obama, either."
He said that both Netanyahu and Abbas "would like to find a way to calm this down and climb down so they are not some how outflanked or undermined by their own extremists."
But complicating that desire is the nature of the violence, which has featured many lone-wolf style attacks, raising questions about how much control Palestinian leaders have over the situation.
"It's going to be very hard to get young, angry Palestinians who want to do violence and engage in terror spontaneously against Israelis ... to turn this off," Miller said.
How the Palestinian leadership handles the situation could be key to its survival, al-Omari said.
"To me, this is symptomatic of a much deeper and much more worrying trend, which is the Palestinian organizations and leaders are losing their legitimacy," al-Omari said. "This is a warning bell of a legitimacy vacuum."