They say the law aims to silence all dissent particularly ahead of a nationwide referendum on the amended constitution expected in January.
In a statement, U.S. State Department spokesperson Jen Psaki said: "We reiterate the concerns we share with civil society representatives inside Egypt that the demonstrations law is restrictive and does not meet international standards. Limiting freedom of assembly, association, and expression will not move Egypt's political transition forward."
The past week, security forces have forcefully broken up several protests by secular activists in Cairo. Police also arrested one of the top secular activists, Alaa Abdel-Fattah, on Thursday for allegedly inciting protests in violation of the law. His wife, Manal Bahy Eldin, also an activist, said police beat her during the arrest.
On Friday, prosecutors ordered Abdel-Fattah detained for four days for investigation, according to Mohammed Abdel Aziz, a member of his legal defense team.
A 50-member panel is amending the Morsi-era constitution drafted mainly by Islamists and passed in December. After months of sessions, largely held behind closed doors, the panel is scheduled to vote on a final draft Saturday but one member, liberal political Mohammed Aboul-Ghar said it may be delayed until Sunday as final controversial articles are worked out.
The panel is supposed to finish its work by Tuesday, under a declaration issued by interim President Adly Mansour soon after the July 3 coup.
The pending referendum could further fuel a backlash. The Islamists reject the entire amendment process and are likely to launch protests against it. Secular activists, meanwhile, are likely to hold their own protests against a charter they say will enshrine military power in politics.
One amendment requires the military's approval of the president's choice for defense minister. The measure effectively allows the military to choose its own leader, giving it considerable independence from the elected, civilian president.
Another article, preserved from the Morsi-era constitution, allows for civilians to be tried in military courts in cases connected to violence toward military facilities or personnel.
Aboul-Ghar said the panel had agreed to remove a controversial article inserted into the 2012 constitution that critics feared would allow a stricter implementation of Shariah law in Egypt.
The article gave a stronger definition to the term "principles of Islamic law," on which Article 2 of the document says legislation must be based. Article 2, which has been in the constitution since the 1970s, will remain in place.
Islamist supporters of Morsi held their latest rallies around the country and in multiple parts of Cairo, most of them numbering in the hundreds. Ten people were wounded in clashes and 183 arrested, according to emergency services and the Interior Ministry.
In Cairo's twin city of Giza, police fired volleys of tear gas to disperse protesters, who burned tires, according to footage of the scene from Associated Press TV. Anti-Islamist residents joined security forces in chasing the Morsi supporters, hurling stones and bottles at them.
Police fired tear gas or water cannons on other Islamist marches in Cairo, the Mediterranean city of Alexandria and the canal city of Suez.
In one protest in eastern Cairo, Islamists chanted, "Down with all killers, down with Abdel-Fattah" referring to army chief Gen. Abdel-Fattah el-Sissi, who ousted against Morsi.
"We don't care about the protest law whatsoever," said Ashraf Abdel-Wahhab, who was participating in a Cairo protest with his wife and eight children. "This is not the first time they attack marches or kill protesters. It's just a cover that they're using."
Secular activists did not hold rallies Friday, aiming to avoid association with the Islamists. The activists oppose the Islamists, seeing them as equally undemocratic as the new government and are wary of being tainted as pro-Brotherhood at a time when a large swath of the public remains eager to crush Islamists.
"Friday is the Brotherhood's day," Mohammed Adel, a leading member of the secular activist group April 6, told the AP. "Even if we had the same cause, we will not protest with them."
Meanwhile, Muslim residents of a village in southern Minya province attacked Christian homes, burning 10 houses and wounding 15 Christians, including a 15 year-old girl thrown from the third floor of a building, according to Ezzat Ibrahim, an activist who monitors minority rights.
Ibrahim said the attack was instigated by rumors of a love affair between a local Christian man and a Muslim woman a factor that can often spark sectarian clashes.