Officials in Cairo earlier this week count ballots from the constitutional referendum.

Story highlights

NEW: Top U.S. diplomat says constitution could be good for Egypt if leaders abide by it

The referendum passes with 98.1% of the vote, electoral commission says

The 38.6% turnout was "unprecedented," the head of the constitutional committee says

Supporters of the Muslim Brotherhood had boycotted the vote

Cairo CNN  — 

Egyptian voters who went to the polls this week have overwhelmingly approved a new constitution, a spokesman for Egypt’s electoral commission announced Saturday in a national broadcast.

The referendum passed handily with 98.1% voting in favor of the new constitution and 1.9 percent voting no, the commission official told reporters in Cairo.

The head of the Egypt Constitutional Committee described the turnout as “unprecedented” – 20 million people, representing 38.6% of those eligible to vote.

Supporters of the now-banned Muslim Brotherhood had boycotted the vote, which took place Tuesday and Wednesday, in response to a continuing government crackdown.

The Brotherhood had supported the country’s first democratically elected president, Mohamed Morsy, who was ousted last July in a military coup.

The Anti-Coup Alliance, composed largely of supporters of Morsy and the Brotherhood, rejected the results in a posting on its Twitter account: “98.1% is not considered a real democracy but a solo dictatorship,” it said.

“If people are arrested for holding ‘vote NO’ posters … should these results be counted?”

The head of the committee heaped praise on this week’s results, calling them a move forward on the path toward democracy.

Rights groups have expressed concern about what they call an increasingly repressive environment in Egypt, where more than 2,200 people have been killed since the ouster of Morsy, who had replaced strongman Hosni Mubarak after he stepped aside in February 2011 amid the massive anti-government demonstrations that were part of the Arab Spring.

Many officials in the international community, too, have spoken out against the Egyptian government’s crackdown on dissenters.

In a statement Saturday, U.S. Secretary of State John Kerry reiterated his own country’s “serious concern about the limits on freedom of peaceful assembly and expression in Egypt.” The new constitution could be a positive milestone for the volatile North African nation, Kerry said, so long as its leaders stand by it.

“It’s what comes next that will shape Egypt’s political, economic and social framework for generations,” Kerry said.

“As Egypt’s transition proceeds, the United States urges the interim Egyptian government to fully implement those rights and freedoms that are guaranteed in the new constitution for the benefit of the Egyptian people, and to take steps toward reconciliation.”

CNN’s Reza Sayah reported from Cairo, and Mohammed Tawfeeq reported from Atlanta. CNN’s Tom Watkins and Greg Botelho contributed to this report.