Boris Johnson is facing calls to meet with footballer Marcus Rashford to discuss his free school meals campaign.
The government has ruled out extending meal vouchers for vulnerable children in England to the holidays, saying it has already increased welfare payments.
But chairman of the education select committee Robert Halfon said a meeting would help ministers create a long-term strategy to combat child food hunger.
Former Tory children’s minister Tim Loughton said he would lobby Number 10.
It comes after Manchester United striker Rashford said he “couldn’t be more proud to call myself British”, as hundreds of cafes, restaurants and some local councils pledged to help feed children facing hardship during the October half term.
Rashford’s petition on child food poverty was approaching 800,000 names on Saturday evening.
On Wednesday, Conservative MPs rejected Labour’s Opposition Day motion to extend free school meals by 322 votes to 261, with five Tory MPs rebelling.
One of those rebels, Mr Halfon, called on Mr Johnson to meet Rashford, telling the BBC: “It may be that they don’t agree with everything that Marcus Rashford is proposing, but it would give us a chance to come up with a long-term plan to combat child food hunger once and for all.”
Meanwhile, Mr Loughton, who did not support Labour’s motion, said the government had a “very proud record” of prioritising help for the poorest in society but added that more needed to be done.
“Notwithstanding this, I still think it would have been easier for the government to continue with the free school meal holiday entitlement in these unprecedented times,” he said.
“I will now lobby ministers to reverse this decision for the Christmas break.
“Voting outright against the government in this debate would have made that task less easy and also (would have) given the hypocritical tactics of the Labour Party more credibility which they didn’t deserve.”
The government extended free school meals to eligible children during the Easter holidays earlier this year.
And following Rashford’s campaign, it bowed to pressure to do the same throughout the summer holiday.
This time it has refused to do so, saying it has given councils £63m for families facing financial difficulties due to pandemic restrictions, as well as increasing welfare support by £9.3bn.
The policy puts it at odds with the other UK nations, which have all extended the policy beyond term time.
Councils that have pledged to support Rashford’s initiative now include those in Manchester, Birmingham, Kensington and Chelsea, and Hillingdon, the local authority for Mr Johnson’s constituency.
Rebecca Horton, owner of the Taste Sandwich Bar in Dingle in Liverpool, said she signed up to Rashford’s campaign because she comes from a deprived area and wanted to support her community.
“I see families struggling, I see children hungry – it was an absolute no brainer for me to jump on the bandwagon, rally round and organise something,” she told BBC Radio 4’s Today programme.
However, MP David Simmonds, who represents Ruislip, Northwood and Pinner, said the scheme “on its own is not going to get the help to people that need it”.
Meanwhile, two Conservative MPs have said comments they made about the issue were “taken out of context” after their remarks were criticised.
Commenting on a school in Mansfield, Ben Bradley said that “one kid lives in a crack den, another in a brothel”. Another Twitter user responded, saying that “£20 cash direct to a crack den and a brothel sounds like the way forward with this one”, to which Mr Bradley replied: “That’s what FSM [free school meal] vouchers in the summer effectively did…”
Mr Bradley said the tweet, which has since been deleted, had been “totally taken out of context”.
He told BBC Breakfast: “I was merely making the point that there are kids who live in really chaotic situations, really difficult lives, where actually giving them an unrestricted voucher to spend on whatever isn’t helpful.”
He said the government had given money to local government which was better placed to provide targeted support, adding: “We need to wrap our arms, as a society, around those families.”
Labour called for him to apologise for the tweet, with deputy leader Angela Rayner saying: “Notwithstanding the fact that the vouchers in summer could only be used to purchase food, this stigmatisation of working class families is disgraceful and disgusting.”
Another Conservative MP, Selaine Saxby, also responded to criticism of comments she made on local businesses giving free food away.
A screenshot of a since-removed post in her name on Facebook said: “I am delighted our local businesses have bounced back so much after lockdown they are able to give away food for free, and very much hope they will not be seeking any further government support.”
The MP later claimed her comments were taken “out of context” and added: “I of course deeply regret any offence which may have been caused.”