"There will be no economy without security and a stable political environment now and in the future," interim Prime Minister Hazem el-Beblawi said, at a government meeting in which the law was discussed, according to the state news agency.
He said some in the opposition aim to create "confusion and sow mistrust between the authorities and the public."
Egypt's powerful military chief, the man who removed Morsi, weighed in as well, urging political factions and the media to support the transition process and line up behind a push to restore security though he did not specifically mention the law.
Political groups should drop "criteria and considerations that don't fit the reality Egypt is living and the challenges it faces," Gen. Abdel-Fattah el-Sissi said, pointing to security threats, including the increasing militant attacks in the Sinai Peninsula.
"The political, economic and social challenges Egypt faces need effort and will and a correct understanding of the requirements of this phase," el-Sissi said at a meeting of officers, according to MENA.
He said a number of measures under way will "correct the democratic path and establish a regime that pleases all Egyptians." It was an apparent reference to the new protest law and a drive to finish amending the constitution.
In the latest violence, attackers on a motorcycle threw a grenade at a police checkpoint near a historic royal palace in Cairo, wounding at least one guard, according to MENA.
Interior Minister Mohammed Ibrahim, in charge of police, insisted the protest law doesn't undermine the right to peaceful expression, as he met with top security officers on how to implement it, starting Monday.
"The law grants the right to organize public gatherings, convoys, and peaceful protests and to join them, in accordance with the law," Ibrahim said according to the state news agency MENA.
Among the restrictions, however, would-be protesters must seek a permit for their gathering three days in advance, which security officials can turn down with little explanation, requiring the applicants to turn to the courts to appeal.
Rights groups, secular political parties and activists, who had lobbied against protest law, said that despite an initial uproar over an earlier draft of the law, the final version had only small changes.
"It gives a legal cover to repression," said the Popular Current, a group led by leftist politician Hamdeen Sabahy, who had backed the removal of Morsi. The group said the law "is not befitting for a country that had two revolts in two years mainly against repression."
In a snub to the law, the youth activist group April 6 and other political groups held a rally outside a central Cairo police station Monday, calling on the government to "eat popcorn!" a joke to say the government is wasting time. They mockingly presented a request to organize a rally they said will be attended by 10 million Egyptians.
The military-backed interim government, meanwhile, is pushing through with a political road map that calls for new presidential and parliamentary elections next year.
The prime minister, el-Beblawi, said Monday that a key first step in the process a referendum on amendments in the constitution will likely take place in the second half of January. He did not give a precise date, which is still to be announced by the interim president.
The 50-member appointed panel is still working on amending the 2012 constitution, mainly drafted by Islamists and approved under Morsi.
The process is also seeing a rising chorus of criticism against the secrecy of its discussions and a number of articles that have granted the next president greater powers, despite calls for checking his authority. It also entrenched the right of the military to try civilians a provision that brought an outcry from many when it was put into the Islamist-backed charter.
