CAIRO — President Mohamed Morsi’s advisers struggled Tuesday to work with a panel of politicians and intellectuals in an effort to work out last-minute proposals that might broaden support for an Islamist-backed draft constitution that is set to go before Egypt’s voters on Saturday, participants said.

Just outside Mr. Morsi’s office, thousands of his opponents staged a seventh night of demonstrations. Many of those against the proposed charter chanted for the downfall of Mr. Morsi, Egypt’s first democratically elected president.

Blocks away, crowds of Islamists denounced the secular opposition’s leaders as murderers for encouraging protests last week that led to deadly clashes with members of the Muslim Brotherhood.

The huge crowds of rivals underscored the animosity and distrust that have all but shut down political dialogue here just as Egypt is poised to complete its promised transition to a constitutional democracy.