Roger Godsiff told the campaigners they had a “just cause” and added: “I will continue to try and fight your corner because you’re right.”
Mr Godsiff, who represents the Hall Green constituency home to Anderton Park Primary School, also criticised the headteacher over the row.
His remarks, made on a video featuring protest organiser Shakeel Afsar, led to calls for the veteran MP to be thrown out of the party.
Angela Rayner, the shadow education secretary, said she had reported him to Labour’s chief whip, Nick Brown.
“This might be the personal views of Mr Roger Godsiff but they do not represent the Labour Party and are discriminatory and irresponsible,” she wrote on Twitter.
Wes Streeting, Labour MP for Ilford North, said he would be tabling a formal complaint to the party.
In a series of tweets, he said: “This made me feel sick to my stomach. One of my own Labour colleagues stood with people who have peddled hatred and bigotry on school gates, intimidating pupils, teachers and parents.
“If he was a Tory MP, we’d be all over it. ”There must be no place for hatred and apologists for hatred in the Labour Party.”
The LGBT Labour group also voted to condemn Mr Godsiff’s remarks and called for the Labour whip to be removed.
“No Labour MP should be pandering to the bigotry we have seen outside the school gates in Birmingham,” the group said on Twitter.
Weeks of protests led to the council obtaining a High Court interim injunction on 31 May banning demonstrations outside the school gates.
A judge is to reconsider the injunction on Monday.
The demonstrators claim the teaching is “over-emphasising a gay ethos”, and have criticised the use of two books, one involving two male penguins who raise an egg, and the other a boy who wears a dress.
Headteacher Sarah Hewitt-Clarkson called the demonstrations “toxic and nasty” and said she has received threats since they started.
Mr Godsiff first waded into the row last month, saying he understood some parents’ concerns about whether the LGBT+ teaching was “age-appropriate” for children as young as four or five
In his latest comments Mr Godsiff said: “If I had the opportunity of rolling the clock back I would do exactly the same thing again.
“Because I think you have a just cause and I regret the fact that it hasn’t been reciprocated by the headteacher.”
Mr Godsiff also asked demonstrators to “consider calling the protest off” before adding: “I will continue to try and fight your corner because you’re right. Nothing more, nothing less. You’re right.
“I will continue to try and work to bring a resolution to this dispute but also to ensure that the school teaches the Equality Act in the same way it is being taught at all the other primary schools – where there isn’t a row.”
Brigid Jones, the Labour deputy leader of Birmingham City Council, responded: “How dare you tell men whose homophobic protests were so threatening and disruptive that they had a court injunction issued against them that they are ‘right’.
“You do not speak for me.”
A petition calling on the constituency Labour Party to deselect Mr Godsiff has gained more than 1,200 signatures.