CARACAS, Venezuela — Humbled by his first electoral defeat, President Hugo Chavez said today he may have been too ambitious in asking voters to let him stand indefinitely for re-election and endorse a huge leap to a socialist state.

"I understand and accept that the proposal I made was quite profound and intense," he said after voters narrowly rejected the sweeping constitutional reforms by 51 percent to 49 percent.

Opposition activists were ecstatic as the results were announced shortly after midnight — with 88 percent of the vote counted, the trend was declared irreversible by elections council chief Tibisay Lucena.

Some shed tears. Others began chanting: "And now he's going away!"

Without the overhaul, Chavez will be barred from running again in 2012.

Foes of the reform effort — including Roman Catholic leaders, media freedom groups, human rights groups and prominent business leaders — said it would have granted Chavez unchecked power and imperiled basic rights.

Chavez told reporters at the presidential palace that the outcome of Sunday's balloting had taught him that "Venezuelan democracy is maturing." His respect for the verdict, he asserted, proves he is a true democratic leader.

"From this moment on, let's be calm," he proposed, asking for no more street violence like the clashes that marred pre-vote protests. "There is no dictatorship here."

A senior U.S. official hailed Chavez's referendum defeat today as a victory for the country's citizens who want to preserve democracy and prevent Chavez from having unchecked power.

"We felt that this referendum would make Chavez president for life, and that's not ever a welcome development," U.S. Undersecretary of State Nicholas Burns told reporters in Singapore. "In a country that wants to be a democracy, the people spoke, and the people spoke for democracy and against unlimited power."

Chavez, who was briefly ousted in a failed 2002 coup, blamed the loss on low turnout among the very supporters who re-elected him a year ago with 63 percent of the vote.

Seven in 10 eligible voters cast ballots then. This time it was just 56 percent.