Police say the blasts were similar to those from fragmentation grenades that killed a man on Friday.
At least 28 people were injured, seven seriously.
Demonstrators are attempting to displace Prime Minister Yingluck Shinawatra and her self-exiled brother Thaksin.
Mr Shinawatra has lived abroad since 2008 to avoid a prison sentence after being convicted of corruption.
They are trying to overthrow the government and stop the upcoming elections in February.
Alan White is a news editor for BuzzFeed News and is based in London.
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