First Minister Alex Salmond announced all children in primaries one to three will be eligible for free meals from next January.
But the SNP group on the city council is demanding the new rules should operate from this August, the start of the new school term.
Nationalist councillors proposed the introduction of free meals in their budget plans in February, but the move was rejected by the ruling Labour group.
SNP finance spokesman Norman MacLeod said: "We were disappointed when Labour chose not to support this proposal last year on cost grounds.
"However I was pleased council leader Gordon Matheson said he supported the idea in principle.
"Now the funding is to be made available, I look forward to the policy being implemented in Glasgow.
"Indeed, I shall be suggesting Glasgow takes a lead on this issue and introduce free school meals for our youngest pupils from the beginning of the school year this August.
"As we have already demonstrated, Glasgow can afford to do this for our young people - all that is required is the political will."
Glasgow already has a substantial numbers of pupils entitled to free meals.
Mr MacLeod said, based on figures he had received from council education officials, the cost of providing free meals between August and January for all P1-3 pupils would mean an additional cost of around £400,000 to £500,000.
England has decided to start funding free school meals from the start of the new school year in 2014.
However, the Scottish Government has said it will provide cash for the move from January next year.
Council leader Gordon Matheson said: "Scotland is lagging behind England.
"While the Scottish Government is waiting until January 2015 to fund free school meals, children in England will be enjoying the benefits from the beginning of the school year in 2014.
"I strongly urge the Scottish Government to use the money they've been given by the UK Government to fund free meals from August 2014.
"Glasgow must also receive our £7 million fair share of this new money.
"For too long the Scottish Government has been reducing Glasgow's percentage share of available local government funding.
"This means we've had our funding cut by an extra £153m over the last two years."