CARACAS — Humbled by his first electoral defeat ever, President 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% to 49%.

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

Some shed tears. Others began chanting: “And now he’s going away!”

Without the overhaul, Mr. 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 Mr. Chavez unchecked power and imperiled basic rights.

Mr. Chavez told reporters at the presidential palace that the outcome of yesterday’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 American official hailed Mr. Chavez’s referendum defeat today as a victory for the country’s citizens who want to preserve democracy and prevent Mr. Chavez from having unchecked power.

“We felt that this referendum would make Chavez president for life, and that’s not ever a welcome development,” 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.”

Mr. 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% of the vote.

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

The defeated reform package would have created new types of communal property, let Mr. Chavez handpick local leaders under a redrawn political map and suspended civil liberties during extended states of emergency.

Other changes would have shortened the workday from eight hours to six, created a social security fund for millions of informal laborers, and promoted communal councils where residents decide how to spend government funds.

A 37-year-old street vendor, Nelly Hernandez, cried as she wandered outside the presidential palace early today amid broken beer bottles as government workers took apart a stage mounted earlier for a victory fete.

“It’s difficult to accept this, but Chavez has not abandoned us, he’ll still be there for us,” she said between sobs.

A close ally of Cuba’s Fidel Castro, Mr. Chavez has redistributed more oil wealth than past Venezuelan leaders, and also has aided Latin American allies — including Bolivia, Ecuador, and Nicaragua — that have followed Venezuela’s turn to the left.

“He is a man who feels for the people, a man who has suffered, a man who comes from below,” a 47-year-old carpenter’s assistant, Carlos Orlando Vega, said outside a polling station in a Caracas slum yesterday.

Mr. Vega is among tens of thousands of Venezuelans who, under Mr. Chavez, have new government-provided homes.

Mr. Chavez urged calm and restraint after his setback.

“I wouldn’t have wanted that Pyrrhic victory,” he said, suggesting a small margin wouldn’t have been enough of a mandate.

Tensions surged in the weeks ahead of yesterday’s vote, with university students leading protests and occasionally clashing with police and Chavista groups.

Mr. Chavez had warned opponents against inciting violence before the vote, and threatened to cut off oil exports to America if the Bush administration interfered.

Mr. Chavez, 53, also suffered some high-profile defections by political allies, including former defense minister General Raul Baduel.

Early today, General Baduel reminded fellow Venezuelans that Mr. Chavez still wields special decree powers thanks to a pliant National Assembly packed with his supporters.

“These results can’t be recognized as a victory,” General Baduel told reporters.

General Baduel, who as defense minister helped Mr. Chavez turn back the 2002 putsch, said Venezuela can only be properly united by convening a popularly elected assembly to rewrite its constitution.

Mr. Chavez has progressively steamrolled a fractured opposition since he was first elected in 1998, and his allies now control most elected posts.

At opposition headquarters in an affluent east Caracas district, jubilant Chavez foes sang the national anthem.

“This reform was about democracy or totalitarian socialism, and democracy won,” opposition leader Leopoldo Lopez said.

“At least now we have the guarantee that Chavez will leave power,” a 22-year-old student who had braved tear gas during street protests, Valeria Aguirre, said.

All was reported calm during yesterday’s voting but 45 people were detained, most for committing ballot-related crimes like “destroying electoral materials,” a chief of a military command overseeing security, General Jesus Gonzalez, said.