White House press secretary Jay Carney says President Barack Obama's administration welcomes "serious calls for national dialogue."
Islamist President Mohammed Morsi has tried to contain the crisis by imposing a state of emergency in three Egyptian provinces.
The Egyptian military has deployed troops in two cities hit by the violence. The main opposition in the country says that Morsi and Islamists have tried to impose a monopoly on power.
At least 56 people have been killed in clashes between protesters and riot police.
Carney said Egypt needs to find a lasting solution that "adheres to the rights of all Egyptians."