Cairo (CNN) -- An Islamist party that once supported Egyptian President Mohamed Morsy met Wednesday with a prominent opposition group to talk about a solution to the political strife that has wracked the country in recent days.
The ultraconservative al-Nour party had backed Morsy and the Muslim Brotherhood, rallying support for the country's new constitution and its emphasis on Sharia law.
Secularists have opposed them.
But on Wednesday, members of al-Nour met with the opposition National Salvation Front, a group composed primarily of non-Islamist parties opposed to Morsy. The two sides are discussing a proposal by al-Nour to end the crisis.
Egypt has been embroiled in violence since last Friday after a series of seemingly unrelated events last week. On Wednesday, protesters faced off against police in downtown Cairo, with police clad in riot gear chasing demonstrators into alleys.
The latest anti-government furor stems from a limited state of emergency declared by Morsy that imposes a 30-day curfew on areas of violence, including the provinces of Port Said, Suez and Ismalia along the Suez Canal.
But on Tuesday, Morsy appeared to back off from his orders, allowing local governments to decide whether to impose the curfew.
Critics have accused Morsy, Egypt's first democratically elected president, of hoarding power.
In a speech this week, he acknowledged the legitimate dissent in Egypt, saying "dialogue is the only way to bring about stability and security." He invited representatives from 11 political parties to a meeting to try to solve the conflict.
But Mohamed ElBaradei, head of the Constitution Party and a member of the National Salvation Front, reiterated two demands before the front would engage in dialogue: the formation of a new government and a committee to amend the constitution.
Morsy on Wednesday was in Berlin, where he referred to the strife in his country during a joint news conference with German Chancellor Angela Merkel.
The Egyptian president said he was working to establish constitutional institutions but vowed not to go beyond what he is empowered to do.
"I don't want to use any extraordinary measures in the transitional period, and I would not allow myself or anyone else to go against the law," he said.
His state of emergency declaration and curfew are "only for one month," and the governors in affected areas retain the power to govern as they see fit, Morsy said.
"Egypt will achieve a state of law and order that we all aspire to," he said. "A civil state that is not run by the military, but its civilians with institutions, with democracy and also the transfer of democracy. A modern country in every sense."
On Tuesday, outgoing U.S. Secretary of State Hillary Clinton said the unrest was not surprising. "It's very difficult going from enclosed regime -- essentially one-man rule -- to a democracy that is trying to be born and learn to walk," she told CNN.
The government must represent all of the people; the rule of law must apply to everyone; and the constitution must not marginalize any one group, she said.
"I think the messages and the actions coming from the leadership have to be changed in order to give people confidence that they are on the right path to the kind of future they seek."
CNN's Ben Wedeman in Cairo and Tom Watkins in Atlanta contributed to this report