US President Barack Obama's administration has been careful to avoid any sign it backs either Ahmed Shafiq
, the ousted Mubarak's last prime minister, or Mohamed Morsi
, the Muslim Brotherhood's candidate.
The pair face off June 16-17 after leading the field in the first round.
Nathan Brown, a Middle East expert at The George Washington University, told AFP he did not believe Obama administration officials necessarily backed the secular Shafiq.
"Shafiq's policies might be ones that they would be more comfortable with but one of the feared outcomes of the United States would be political chaos and a Shafiq victory might be more likely to provoke that," Brown said.
Seen by some voters as a man who would restore pre-revolutionary order, Shafiq is also perceived as illegitimate by many of the people who took part in the revolution that ousted Mubarak in February last year, he said.
In a sign of the feared instability Brown mentioned, protesters set fire Monday to Shafiq's headquarters after the election committee said he had made it into a run-off vote with Morsi.
And if he wins, he added, Shafiq will not "be quite as cooperative with the United States as Mubarak was because domestically he would be far, far weaker."
Shafiq may also be a reluctant partner because he might feel Washington had betrayed the Mubarak regime.
In Washington, both Morsi and Shafiq "set off almost mirror-image anxieties, one about the result for Egypt and the other about the fate of American-Egyptian relations," Brown said.
Though his own ties with US ally Israel were often tense, Mubarak at times cooperated with Israel on security matters and aided US-brokered negotiations between Israel and the Palestinians.
Mubarak also sent troops in support of the US-led coalition that drove Iraqi troops from Kuwait in 1991, worked closely with the United States on counter-terrorism and strongly opposed Iran's regional ambitions.
In contrast, the Brotherhood and Washington have long disagreed on Iran, regional security cooperation, "the American military presence in the region and most of all on Israel," Brown said.
If Morsi wins, "there is little doubt that close Israeli-Egyptian security cooperation... would be absolutely out of the question," the professor said.
Marina Ottaway, an analyst with the Carnegie Endowment for International Peace, added: "What has been a cold peace between Egypt and Israel is going to become even colder if the Brotherhood wins.
Nonetheless, analysts said, both candidates will seek to preserve the peace treaty with Israel for their own reasons.
Morsi will accept that the US-backed military and security apparatus will still have a voice in foreign affairs, including on Israel, and will put a priority on tackling domestic issues like the troubled Egyptian economy.
Shafiq will try to continue Mubarak's foreign policy, but will face more pressure from anti-Israeli public opinion, Ottaway said.
"And I think the relationship with the United States is going to be much more difficult no matter who wins," she said.
If Washington is seen as backing Shafiq, it would look like it "is still backing the old regime and that would undermine the credibility of the US not only in Egypt but throughout the Arab world," Ottaway told AFP.
The Council on Foreign Relations' Steven Cook said it would be "politically unpragmatic" for the Brotherhood to embrace the United States, but it might work with Washington in "the short run" to help tackle its economic crisis.
Things will not be necessarily easier if Shafiq wins, he agreed.
"I don't think that Washington has any preference, and if it does, it is certainly not broadcasting it to the world. The United States hopes to be able to work with whoever is the next president, but it is going to be hard."