Venezuelan President Hugo Chavez has said he may have made a mistake in the timing of his planned constitutional changes, rejected by voters on Sunday.
Mr Chavez, speaking to state TV, said it was possible that Venezuela was not yet mature enough for socialism.
Venezuelans voted 51% to 49% against the proposals, which included ending presidential term limits.
US President George W Bush said the Venezuelan people had rejected one-man rule and voted for democracy.
Other proposals would have allowed Venezuela's president to appoint local leaders under a redrawn political map and ended the central bank's autonomy.
Also proposed were a reduction in the working day to six hours, creating a social fund for informal workers, and further establishing community councils where residents can decide how to spend government money.
The fractured opposition managed to mobilise its base
The result surprised both the opposition and government camps.
Opponents to Mr Chavez appeared to have turned out in large numbers after a campaign led by students, who have become the most prominent voices of Venezuelan opposition.
But with an abstention rate of 44%, it seems that while some of Mr Chavez's supporters may still back him, they were less convinced by his proposed reforms.
President Chavez admitted that he needed to analyse why some of those who turned out to re-elect him with 63% of the vote last December did not turn out on Sunday.
And speaking to Venezuelan TV on Monday, Mr Chavez also admitted that it was perhaps not the right time to push through his socialist project.
"Perhaps I made a mistake in the timing of my proposals, that could be, that we are not politically mature enough," he said.
"It's a challenge for us, we're going to convince those of our comrades who have doubts, those who have fears concerning socialism."
But Mr Chavez has stressed that the battle to build socialism will continue and his reform proposal is still "alive".
The referendum result does not mean that Mr Chavez is losing his strong grip on power, BBC Americas reporter Julian Miglierini says.
The president's supporters still dominate the national assembly, a law passed in January allows him to govern by decree and his current presidential mandate lasts until 2013.
Indefinite re-election of president, term increased from 6 to 7 years
Central Bank autonomy ended
Structure of country's administrative districts reorganised
Maximum working day cut from 8 hours to 6
Voting age lowered from 18 to 16
Social security benefits extended to workers in informal sector
Gen Raul Baduel, a former defence minister and ex-Chavez ally, urged the opposition to remain vigilant against further attempts to introduce reforms.
"We need to remain conscious of the possibility that the president could attempt to reach the same results through the legislative process," he said. Among international reaction was a message from Cuban leader Fidel Castro who said his ally had shown "courage" and "dignity" in accepting defeat.
Bolivian President Evo Morales, who is also trying to change his country's constitution, said: "If (Mr) Chavez were a dictator, he would never have presented his reforms to the people for consideration.
Asked about the referendum result, President Bush said on Tuesday that "a vote for democracy" had taken place.