Cairo (CNN) -- Egypt's deeply divided political strife took another turn Wednesday, as an Islamist party that had supported the president met with a prominent opposition group to talk about a solution.

The ultraconservative Salafi Nour party once backed President Mohamed Morsy and the Muslim Brotherhood, rallying support for the country's new constitution and its emphasis on Sharia law.

With few exceptions, the political scene was quickly divided between Islamists and secularists.

But on Wednesday, members of the party met with the National Salvation Front, a group of mainly non-Islamist parties that has decried Morsy's tenure. The two sides are discussing a proposal by Salafi Nour to end the crisis ravaging the country.

Parts of Egypt have been embroiled in fresh violence after a series of seemingly unrelated events last week.

The latest anti-government furor stems from a limited state of emergency declared by Morsy that implements a 30-day curfew for violent hot spots, including the provinces of Port Said, Suez and Isamalia along the Suez Canal.

But on Tuesday, Morsy appeared to back off from his orders, allowing local governments to decide whether they wanted to implement the curfew.

Critics have accused Morsy, Egypt's first democratically elected president, of power hoarding.

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 opposition National Salvation Front, reiterated two demands before the National Salvation Front would engage in a dialogue: the formation of a new government and a committee to amend the constitution.

Morsy on Wednesday was in Berlin, where he referred to some of the strife in his country during a news conference with German Chancellor Angela Merkel.

The Egyptian president said that he is working to establish constitutional institutions and that he would not go above the law to achieve that.

"I don't want to use any extraordinary measures in the transitional period," he said.

His state of emergency declaration and curfew are "only for one month," and the governors in those areas still have 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."