Rice - who is on the first leg of a tour of the Middle East - also met foreign ministers from Egypt, Jordan, Saudi Arabia and the United Arab Emirates to urge them to begin negotiations with Israel.
"It is really sad to see Egypt - a republic - turned into a kingdom"
Be Humble, UK
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The proposed constitutional changes would enshrine tough anti-terrorism laws into Egypt's constitution - something opponents say could lead to continued police and judicial abuses.
They also would outlaw political parties based on religion, blunting the country's main opposition group, the Muslim Brotherhood, who have called for a boycott of the referendum.
Hundreds of opposition supporters took part in a demonstration against the reforms in Cairo on Sunday.
Ahmed Aboul Gheit, the Egyptian foreign minister, standing next to Rice at a press conference following the talks, defended the proposed constitutional changes, saying Egypt faced a threat from "a number of hardliner and extremist types."
Rice said George Bush, the US president, remained committed to spreading democracy in the Middle East.
"The process of reform is one that is difficult - it's going to have its ups and downs," she said.
"We recognize that states do this in their own way."
Before leaving for Israel on the next leg of her tour, Rice called on Arab states to seeks for ways to revive peace talks with Israel ahead of their annual summit next week.
"I would hope that every state would search very deep to see what it can do at this crucial time to finally end this conflict," Rice said.
Rice has been hoping to revive a dormant plan for a broad Arab-Israeli peace put forward by Saudi Arabia five years ago.
The pan-Arab body's 22 members are expected to discuss the initiative at their two-day annual summit, due to begin on Wednesday in Riyadh.
Aboul Gheit however said the impetuous for new negotiations should come from Israel.
"Egypt is committed to this initiative and we hope the other party, the Israeli side will deal with the initiative in a positive manner," he said.
"We should wait for the Israeli side and then we move ahead towards negotiations."