Salma Yaqoob and Mohammed Ishtiaq remained seated during a ceremony for Lance Corporal Matthew Croucher.
The 26-year-old was awarded the George Cross after he flung himself onto a Taliban hand grenade to save his comrades during an ambush in Helmand Province in 2008.
He was serving with 40 Commando when his patrol came under fire but he miraculously survived because his backpack took the force of the blast.
L/Cpl Croucher became the most highly-decorated serving Marine when he received the George Cross for ‘outstanding bravery not involving direct contact with the enemy’.
More than 100 councillors at Birmingham City Council attended a meeting on Tuesday night to honour L/Cpl Croucher, who was there as guest of honour.
But when the councillors stood to give him a standing ovation Cllrs Yaqoob and Ishtiaq, who are both members of the Respect party, refused to get to their feet.
Fellow councillors today reacted with fury at the snub and branded the pair 'shameful'.
Conservative Cllr John Lines said: 'They should be ashamed of themselves.
'This was not the time or place to stage an anti-war protest - this man risked his life for his comrades.
'I was happy to give this hero a standing ovation and I have invited him to be guest of honour when we open new houses for ex-military personnel later this year.'
Conservative Cllr Peter Douglas Osborn added: 'As far as I am concerned it is no longer the Respect Party, but the disrespect party.'
L/Cpl Croucher, from Solihull, West Midlands., who now runs a security firm, was at the meeting to highlight his work with the Royal British Legion.
He said: 'Obviously not everyone is behind the work we are doing in Iraq and Afghanistan and they have their point of view.
'On the other hand, it was nice to be shown respect for the job we do by the overwhelming majority of councillors.'
Yaqoob and Ishtiaq yesterday remained defiant about their decision to snub L/Cpl Croucher, branding the gesture 'false patriotism'.
Cllr Yaqoob, Respect Party leader and head of Birmingham’s Stop the War Coalition, said: 'It was more about the politicians feeling good about themselves for sending our young men to fight for reasons that have proved to be false.
'I have every sympathy for our soldiers on a human level, they are only doing their jobs.
'But this ovation was just a big public show, it was false patriotism.
'Wrapping coffins in the flag and awarding medals does not make it right.'
Cllr Ishtiaq added: 'At the end of the day, if these so-called politicians want to give a standing ovation, why don’t they go and fight themselves?
'What we did was out of principle.'
The mother of L/Cpl Croucher expressed shock that two Muslim councillors snubbed her son.
Margaret Croucher said: '
It is a surprising thing to have happened. I don't think Matt expected to be caught in the middle of a row.
'I am disappointed but like Matt said after it happened, everyone is entitled to their opinion whatever it may be.'
Cllr Salma Yaqoob, 38, a married mother-of-three, was elected to Birmingham City Council in 2006 and represents the Sparkbrook ward.
She received nearly 50 per cent of the vote which is one of the highest majorities of any councillor.
Cllr Mohammed Ishtiaq, 35, is a married father-of-one, was elected to the council in 2007 and also represents the Sparkbrook ward.
Today he defended the decision to snub L/Cpl Croucher's standing ovation.
He said: 'We had no idea that there would be a standing ovation. It was announced at the start of the meeting.
'We were caught unawares but we decided we did not wish to take part.
'We acknowledged Matt Croucher by nodding and smiling in his direction which I think he appreciated.
'We were protesting against the other politicians not against Matt.
'He is a hero for what he did but he, like many other young men and women, are in a war which is based on a pack of lies.'
A Birmingham City Council spokesman said the councillors had not breached any rules and would not comment on political matters.
Is The Respect Party an Al Qaeda propaganda unit ?