The post attracted hundreds of critical comments from the public, opposition politicians and journalists.
Mr Soares, 66, resigned after Prime Minister Antonio Costa reprimanded him and issued a public apology.
"I won`t relinquish my right to express an opinion," Mr Soares said in a statement.
He also said he did not want to create problems for the centre-left Socialist government, which took power in November.
Mr Soares, a former mayor of Lisbon and the son of a former Portuguese prime minister and president, has long been a polarising figure, the BBC`s Alison Roberts in Lisbon says.
One of the articles in the Publico newspaper he was responding to in Thursday`s controversial post (in Portuguese) accused him of incompetence, rudeness and cronyism.
He initially defended his comments as a response to an "insulting personal attack", but later apologised.
"I am a peaceful man," he said.
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