The Scottish Government is expected to be defeated at the vote on Wednesday as all opposition parties oppose the tests, which some teachers have said left pupils in tears.
In an interview on the BBC’s Sunday Politics Scotland programme, Mr Swinney repeatedly refused to say whether or not he would scrap the tests in the event of a government defeat on Wednesday.
He was asked “If parliament votes to scrap them, will you scrap them?”
He replied: “We’ll see what parliament comes up with on Wednesday.
“Parliamentary motions are not binding on the government, the only thing that’s binding on the government is legislation.
“So, we’ll reflect on whatever parliament produces on Wednesday in the debate but we will make the very strong, evidenced argument for primary one standardised assessments because it’s part of the integral process of learning for young people within Scotland and it’s important that we identify at the earliest possible opportunity the needs of young people and support them to overcome those challenges.”
He was repeatedly pressed on the issue of the vote but would not give a definitive answer.
Scottish Labour’s education spokesman Iain Gray described Mr Swinney’s answers as a “thinly veiled threat to ignore the will of the Scottish Parliament” while Scottish Liberal Democrat leader Willie said they were an “astoundingly arrogant intervention”.
Mr Gray urged the education secretary to listen to teachers who believe the tests are “useless”, adding: “It’s time for Mr Swinney to put the children of Scotland ahead of his ego and bin these tests.”
Scottish Lib Dem leader Willie Rennie added: “I’ve worked all my life for a democratic Scottish Parliament and I find it astonishing that a Government minister could contemplate plowing onward if parliament expressly instructed him to stop.”
Scottish Green education spokesman Ross Greer said if the parliament votes as expected against the tests, “there’ll be no justification for John Swinney to ignore the tide of evidence and the strength of feeling against this deeply misguided government policy”.