Mr Brookes said some parents leave children early and collect them late
The leader of the National Association of Head Teachers (NAHT) has said some parents "dump" their children on schools for up to 10 hours a day.
Mick Brookes, at the union's conference in Liverpool, said some parents were "abdicating their responsibility".
But Children's Minister Beverly Hughes, who was jeered when the issue of league tables and tests were raised, said his remarks were untrue and unhelpful.
Mr Brookes later refused to rule out a national boycott of the Sats tests.
The union leader said the testing system for seven, 11 and 14 year-olds was "expensive nonsense" and called for pupils to be measured primarily by internal teacher assessments from next year.
The government plans to replace Sats tests in 2011 with a new system that is currently being piloted.
However, NAHT delegates have warned that the proposed change could see pupils taking even more tests than they do now.
Where the issue of parents is concerned, Mr Brookes said there are a large minority of mothers and fathers who do not understand how to be good parents.
And he accused a smaller minority of abandoning their children at schools and nurseries.
He told a news conference: "These parents dump their children early in the morning and are late picking them up - we do believe some are abdicating their responsibility to their children."
But Ms Hughes said she thought that was untrue and unhelpful.
New extended schools will offer care from 0800 until 1800.
However, the minister said it was up to parents to decide how long they left their children, adding that most parents were trying to do their best by their children.
Ms Hughes was jeered following an exchange with Rona Tutt, a delegate from Hertfordshire, who asked the minister what she was going to do to reform the "test-ridden education system".
Ms Hughes responded by saying headteachers' views were important "but it's not the only perspective".
She said: "The views of parents are also important."
The remark provoked noisy protests from the conference as delegates interrupted the minister with shouting and jeering.
The minister said: "Let me finish. I'm sure you will do me the courtesy of letting me finish."
And Ms Hughes told delegates that parents and the public wanted test results and tables to show how pupils and schools were performing.
However, delegates repeatedly shouted "No" at the minister during the following questions and answers, with one person calling out "rubbish".
Later, the minister denied being jeered and said there had been "a very constructive discussion".
Where testing was concerned, the minister said: "We are not going to take away the ability of parents to know how their children are doing."
In an interview with BBC News, Ms Hughes addressed the issue of Ofsted inspections, following research by the NAHT which suggests Ofsted inspection pressures deter talented teachers from taking on the top jobs in schools.
Ms Hughes said next year Ofsted would be "consulting with schools about how we can make progress in terms of the regime", such as using shorter tests, adding that she wants the inspections to be less "narrow" to reflect all aspects of school life.