About 5,000 soldiers and police have been sent to guard the special polls.
Goltiao, a police chief on the southern island Mindinao, also said seven blasts were heard before balloting started in Masiu town.
"No one was hurt in these explosions. Some groups might be trying to scare people from casting their ballots."
Two people were injured when gunmen opened fire at schools in the towns of Pantar and Kapai, Goltiao said.
ABS-CBN television reported fist-fights among poll watchers of rival candidates who swapped accusations of manipulating the ballot in Kapai township.
The report said there was also an attempt to let a child vote, and the head of a poll watchdog group saw one voter casting ballots three times.
The National Citizens' Movement for Free Elections (NAMFREL) said results from the polls could help decide the last two slots in the race for 12 seats in the upper house of congress.
Unofficial ballot results from NAMFREL and the Commission on Elections showed the opposition is leading the contest with eight slots, followed by two pro-government candidates and two independents.
But four allies of Gloria Arroyo, the country's president, were trailing by about 100,000 to 500,000 votes and with four million ballots from the south still to be tallied - pro-government candidates stand a high chance of winning.
Although the national tally is incomplete from local and congressional elections, pro-government parties say they won more than 190 of the 220 district seats in a 275-member house of representatives.
Fifty-five seats were still being contested by 93 party-list groups.
The pro-government side's expected success will insulate Arroyo from a third impeachment motion during the rest of her final term, which runs out in 2010.
She has failed to shake allegations that she cheated in the 2004 presidential elections.
But a victory by the opposition in the Senate could block Arroyo's key legislative agenda.