Saturday, the leaders of Egypt's ruling party resigned, including Mubarak's son, who was seen as a possible replacement should the president step down.
In Sunday's meeting, the two sides agreed to set up a committee of judiciary and political figures to study proposed constitutional amendments among other changes.
The regime also pledged not to harass those participating in the anti-government protests, which have drawn hundreds of thousands at the biggest rallies. The government also agreed not to hamper freedom of press and not to interfere with text messaging and Internet.
The committee has until the first week of March to finish the tasks.
Meantime in Los Angeles, demonstrators rallied outside the federal building in Westwood Saturday, calling for Mubarak to step down immediately.
Mubarak, Egypt's ruler of nearly 30 years, has rejected calls to step down immediately and instead promised a package of unspecified political reforms - part of a series of concessions the regime has made in an unsuccessful bid to quell the protests.
Demonstrators think an orderly transition can take place only after he leaves office. They were not impressed with the resignations of Egypt's ruling party leaders.
In an interview with the Christian Broadcasting Network, Palin said the administration should, "level" with the American people on what it knows about the crisis in Cairo.
She also said that the U.S. should not stand behind a government led by the Muslim Brotherhood.