Police Sergeant Major Narong Pitisit, 45, died of injuries sustained in the clash with opposition protesters at the Thai-Japanese Stadium, where candidates were filing their nominations for the elections.
Medical officials said he was shot in the chest and suffered severe blood loss. Nearly 100 people, including policemen, were injured during clashes.
In a statement, the EC said its recommendation to delay the polls was due to the violence that started after police fired teargas and rubber bullets at stone-throwing mobs trying to enter the stadium.
But, Premier Yingluck Shinawatra's government rejected the EC's call for delay in the polls. "The Election Commission said holding elections will bring violence but the government believes delaying an election will cause more violence," Deputy Prime Minister Phongthep Thepkanjana said.
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The opposition Democrat Party has already announced its plans to boycott the polls.
The protesters have been demanding Yingluck's resignation since mid-October. The protests began after the government tried to introduce an amnesty bill that would have paved the way for the return of her brother, former premier Thaksin Shinawatra currently in self-exile in Dubai.
Yingluck called the snap election, scheduled for 2 February, after weeks of protests. The demonstrators dismissed the election, and the official opposition has refused to field candidates. Protesters have further rejected another offer by Yingluck to form a national reform council intended to run alongside her government.