By Warren Strobel and Phil Stewart
WASHINGTON (Reuters) - With Egypt and its democratic experiment at a tipping point, U.S. President Barack Obama finds himself trying to nudge the most populous Arab country's bitterly divided antagonists toward compromise but finds his influence limited.
Where Obama and his predecessors once dealt with a single all-powerful figure - ousted strongman President Hosni Mubarak - the White House is now gingerly trying to persuade unpopular, but democratically elected, President Mohamed Mursi and Egypt's military to strike a political deal, all without alienating millions of Egyptians protesting in the streets.
Egypt's size and leading position in the Arab world mean its political course will be felt throughout the region, where the United States is already struggling to stem Islamist militants and sectarian strife.
But Obama has not forged close ties to Mursi, and has been criticized for what is widely seen as his standoffish approach to Egypt's attempts to solidify its democracy.
Now that Egypt looks to be on the brink of chaos, an immediate challenge for Washington is how to sway the country's armed forces, which have given Mursi until Wednesday to agree on power-sharing with other political forces, warning it would set out its own roadmap for the country's future if he did not.
A military coup against Mursi and his crumbling government would seriously undermine Obama's promotion of democracy in the Middle East and could lead to a cutoff in U.S. military aid to Egypt.
The United States relied heavily on its ties with Egypt's top military officers, forged through decades of joint training, military schooling in the United States and U.S. military aid, to guide the country to free elections when protesters poured into Cairo's Tahrir Square in early 2011 demanding Mubarak's ouster.
The armed forces eventually sided with the protesters, hastening Mubarak's downfall. The difference this time is that Mursi was democratically elected in a process backed by Washington.
U.S. influence with the Egyptian military is greatest on regional security matters, such as Egypt's peace treaty with Israel.
"Nobody should be under the illusion that simply because we give $1.3 billion of weapons and training support to the Egyptian military that we can control them in any way when it comes to internal politics and the internal security situation," said Brian Katulis at the Center for American Progress, a Washington-based think tank.
Underlying the importance for Washington of keeping ties to Egypt's military, Kerry in May quietly approved $1.3 billion in military assistance, despite the country's failure to meet democracy standards set by the U.S. Congress. To do so, he waived a U.S. legal requirement that he certify the Egyptian government "is supporting the transition to civilian government, including holding free and fair elections, implementing policies to protect freedom of expression, association and religion, and due process of law."
Army General Martin Dempsey, chairman of the U.S. Joint Chiefs of Staff, spoke by telephone this week with Egypt's army chief of staff, Lieutenant General Sedki Sobhi, a U.S. defense official said.
Details of that conversation were not released, and it is unclear whether Dempsey or other top U.S. officials have explicitly warned the Egyptian military against mounting a coup.
But neither have Obama, Secretary of State John Kerry or other U.S. leaders publicly criticized the army's ultimatum.
Michele Dunne, a former State Department official who served in Egypt and Israel and is now at the Atlantic Council think tank, said the key question is whether the military sweeps Mursi and his government aside entirely and steps in to rule, or stops short of that - perhaps by appointing a civilian figurehead.
The U.S.-Egypt military relationship was tested when the army assumed power after Mubarak's fall, and "if the military takes control, it's going to be tested again," she said.
OBAMA: LISTEN TO DEMONSTRATORS
The Obama White House has not been enamored with Mursi, a leader of the Islamist Muslim Brotherhood whom it sees as having failed to form an inclusive, effective government. Obama has not hosted Mursi at the White House, and officials canceled a visit by the Egyptian leader last year after a video from 2010 surfaced in which Morsi described Israelis as "descendants of apes and pigs."
Obama, wrapping up an Africa tour, called Mursi on Tuesday, according to the White House. "Democracy is about ... ensuring that the voices of all Egyptians are heard and represented by their government, including the many Egyptians demonstrating throughout the country," a White House statement said. Obama told Mursi that "the current crisis can only be resolved through a political process."
But amid reports of violence, Mursi showed little sign of compromise, calling on the military to withdraw its ultimatum and saying he would not be dictated to.
For Washington, communicating with the Mursi government is becoming more problematic.
State Department spokeswoman Jen Psaki announced Tuesday that Kerry had called Egyptian Foreign Minister Mohamed Kamel Amr, only to be reminded by reporters that Amr had reportedly tendered his resignation - one of a half-dozen or so senior Mursi aides to resign in recent days.
It was unclear whether Amr was still in his position when Kerry spoke with him, giving a sense in Washington that the Mursi government is unraveling.
DOUBT ABOUT U.S. DEMOCRATIC COMMITMENT
As with the civil war in Syria, Obama has been criticized for what many analysts say is a largely hands-off approach toward post-Mubarak Egypt.
Obama administration officials counter that Washington has limited influence on Arab societies struggling to remake themselves, and too overt a U.S. intervention would backfire.
In the latest crisis, the United States, seen for decades in the Arab world as a supporter of pro-Western autocrats, has insisted it is not playing favorites.
That has not stopped some among the millions of protesters on Egypt's city streets from criticizing what they see as Washington's backing for Mursi. Photos insulting U.S. Ambassador to Egypt Anne Patterson have appeared in the crowds.
Obama told Mursi in their phone conversation "that the United States is committed to the democratic process in Egypt and does not support any single party or group," the White House said.
Dunne said popular resentments at the United States can be blamed in part on policies toward Egypt and other fragile Arab democracies that she labeled "unimaginative at best."
"We could have done so much more to encourage the transition in Egypt," she said. "We really have stayed out, stayed on the sidelines, waiting to see what happened."
(Editing by Alistair Bell and Prudence Crowther)