Morsi on Sunday was declared the winner of a divisive presidential run-off, making him the first elected leader of the Arab world's most populous nation since a popular uprising ousted longtime president Hosni Mubarak last year.

"Egypt has taken another halting step toward democracy -- and avoided a plunge into chaos," the Washington Post said in an editorial, praising the military for recognising Morsi's victory over ex-premier Ahmed Shafiq.

The Wall Street Journal offered a similar take, saying in a commentary: "The road to democracy remains uncertain, but this presidential election is a qualified step forward."

The New York Times called Morsi's win an "ambiguous milestone in Egypt's promised transition to democracy" in its report.

The Journal cautioned that Morsi, the Muslim Brotherhood's candidate who resigned from the group to take the top job, would have to allay popular fears about his government's intentions.

"A majority supported someone else in the first round of the elections, and in the runoff they rejected the return of the old regime represented by Mr. Shafiq. Egyptians weren't voting for an Islamist state," it said.

The Brotherhood has rejected a constitutional declaration by the military that dissolves the Islamist-led parliament and gives the army a broad say in government policy and control over the new constitution.

The Washington Post warned the country's political situation was far from resolved even though an election winner had been declared.

"Whether that development becomes a foundation to build on or a prelude to further destabilisation" in Egypt "will depend on whether the military and Islamists can find a modus vivendi based on democratic principles," it said.

The Journal noted: "One undesirable outcome going forward would be a military establishment that lets the Brotherhood slowly Islamicise the country in return for keeping power. The world can do without an Arab Pakistan."

The Post called on the United States to wield its influence over Egypt's military -- which receives more than $1 billion in US aid each year -- to ensure that Morsi is given "full governing power".

"Egypt still has a chance to complete a democratic transition, but it will require more mature political behavior by all sides," the Post concluded.

"Strong encouragement by the United States -- particularly to the recalcitrant generals of the old order -- can help."

For the Journal, "a new legitimately elected president is a good democratic start, but only that."