Rebels had threatened to disrupt the Saturday voting on 15 proposed administrative reforms, including whether to reduce congressional seats from 268 to 218 and to deprive public servants found to have committed state fraud of their civil rights.
Colombians also were to decide whether to freeze public servants' salaries and state spending for two years from 2004, and on limiting functionaries' pensions and privileges.
President Alvaro Uribe appeared set to receive a ringing endorsement of his proposals in early official returns - with nearly 97% of the vote counted, each of the 15 proposals was passing with yes votes of between 80% and 93%.
It was unclear, however, whether the turnout was large enough to meet the threshold of 25% of the electorate needed to make the referendum valid.
So far, turnout on all the questions was 24.75% or less.
On Sunday, voters will elect mayors, municipal councils, governors and delegates to local assemblies for a three-year mandate.
About 300,000 troops and police have been deployed to provide security for the weekend voting.
Meanwhile, authorities blamed the leftist Revolutionary Armed Forces of Colombia, known as FARC, for attacks that resulted in the deaths of six police officers and an army officer at Jambalo, 600km southwest of Bogota. Eight others were wounded.
National police director General, Teodoro Campo, said four were killed in the initial attack and two officers brought in as reinforcements died in an ambush.
A separate grenade attack killed an army sergeant at a military barracks in the central province of Tolima, 100km west of Bogota, officials said.
Later, six people were killed and 10 wounded when a bomb exploded at a dairy in northern Colombia.
Thirteen people have died in
The explosion at the Colanta dairy cooperative at Yarumal, 550km north of Bogota, was the second at the cooperative since 6 September, when a dynamite blast injured three people.
Caracol radio reported the blast may have been linked to an attempt at extortion rather than the referendum.
FARC rebels also kidnapped 12 poll monitors in Trujillo, 500km southwest of Bogota, and set fire to voting booths, authorities said.
Shortly after voting started, a bomb went off near a polling station in Colombia's second largest city, Medellin, injuring one person. A member of the leftist party Polo Democratico was kidnapped under circumstances that were unclear.
Ahead of the vote, Uribe said his aim was to defeat the "terrorists... any way we can."
Uribe was elected promising a hard line against rebel groups. He said a successful referendum would allow him to defeat FARC and National Liberation Army leftists.
Uribe has promised to crack down
against rebel groups
But at least 204 candidates for Colombia's 1098 city councils and 32 provincial governments withdrew after threats from rebels, the association of municipalities said. Uribe ordered election authorities not to strike their names from the ballots for Sunday's vote.
Uribe has lobbied hard in recent days for the referendum in radio and television appearances. The finance ministry said the measures could save 10 billion dollars through 2010.