Egypt in crisis
The struggle to save Egypt's revolution
Is Egypt heading for holy war?
Coup or no coup?
The US has urged Egypt's leadership to stop the "arbitrary" arrests of Muslim Brotherhood members, warning against targeting any particular group.
"You're working against yourself if your effort is to be inclusive," White House spokesman Jay Carney said.
UN chief Ban Ki-moon also warned against the exclusion of any party.
Rival rallies are expected in Cairo on Friday amid rising tensions over the army's overthrow of Islamist President Mohammed Morsi last week.
Supporters demanding Mr Morsi's reinstatement have continued to stage mass protests in Cairo this week near the barracks - where he is believed to be being held.
There is no place for retribution or the exclusion of any major party”Ban Ki-moon
On Thursday, the Obama administration and UN both raised concerns about Egypt's decision to issue arrest warrants for the leader of the Muslim Brotherhood - to which Mr Morsi belongs - and nine senior figures of the movement.
"The only way this is going to work successfully... is if all parties are encouraged and allowed to participate and that's why we've made clear that arbitrary arrests are not anything that we can support,'' Mr Carney said.
Mr Ban "made clear that there is no place for retribution or for the exclusion of any major party or community in Egypt," in a telephone call with Egypt's Foreign Minister Kamel Amr on Thursday.
US state department spokeswoman Jen Psaki voiced even harsher criticism, saying the arrests contradicted reassurances they had received by the Egyptian military and authorities of inclusivity.
US policy makers would monitor the situation closely as they review decisions on assistance to Egypt, she added.
While the White House has not yet publicly confirmed comments by unnamed US officials that it will go ahead with a planned delivery of four F-16 fighter jets to Egypt, spokesman Jay Carney said that the administration did not believe it should immediately suspend aid to Egypt.
Meanwhile, tensions continue to rise as Brotherhood leaders urge supporters to attend mass rallies across Cairo on the first Friday of Ramadan.
Rival protests are planned for Tahrir Square, including a mass iftar - breaking the fast.
On Thursday the Muslim Brotherhood vowed to continue "peaceful resistance to the bloody military coup against constitutional legitimacy".
Mr Morsi's removal - a year after he was elected - followed protests by millions of people across Egypt.
While the new authorities have have not specified where Mr Morsi is, a foreign ministry spokesman has said he is in a "safe place" and being treated in a "very dignified manner".
However, dozens of people have died in deadly clashes in the aftermath of his ousting. On Monday alone more than 50 Morsi loyalists were killed in clashes with the army.
Adly Mansour's transition timeline
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Key players in the Egyptian crisis
Profile: Hazem el-Beblawi
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The Muslim Brotherhood's spiritual leader, Mohammed Badie, and nine other senior figures were charged on Wednesday with inciting Monday's violence, despite conflicting accounts of the incident.
Correspondents say the new warrants could scupper any attempts to persuade the Brotherhood - banned for decades under former President Hosni Mubarak - to participate in the transitional political process announced by interim President Adly Mansour this week.
The Brotherhood's political wing, the Freedom and Justice Party (FJP), says it will turn down a post in the cabinet being formed by the interim Prime Minister Hazem al-Beblawi.
Meanwhile, Mr Beblawi said on Thursday that he had still not ruled out offering posts to the FJP.
"I don't look at political association," he told the AFP news agency. "I'm taking two criteria for the next government. Efficiency and credibility."
The main liberal opposition coalition, the National Salvation Front (NSF), and the grassroots Tamarod protest movement, which co-ordinated the anti-Morsi protests, said they were not consulted on the constitutional decree and had concerns about it.