Conservative Jack Lopresti backs Stoke Gifford Parish Council's decision to demand a fee from the group for using Little Stoke Park.
Speaking in the Commons, he said it was not a "matter of central government".
It comes after Greg Clark, Secretary of State for Communities and Local Government, wrote to the council asking it to reconsider its decision.
The authority is the first to say it wants to charge Parkrun a fee for the use of its grounds.
Councillors voted in favour of charges for "wear and tear", on the grounds that it was unfair to expect non-running residents to pay for the park's upkeep.
But the decision sparked a national outcry, and an online petition against the plans has topped 51,000 signatures.
In his letter to council chairman Ernie Brown, Mr Clark said he would consider using legislation to stop the authority from charging for organised sporting events.
He argued that said local parks were "community assets" and there is a "long tradition" of free use for public parks.
He also said there was "no issue" with local authorities charging for the use of park facilities, but the decision should be "transparent and accountable".
However, Mr Lopresti, who represents the Filton and Bradley Stoke ward, said: "The decision of [the council] to charge Parkrun for the use of its park is not a matter of central government and this should remain the case."
He added that Parkrun has "become a victim of its own success" and it "overwhelms the local facilities it needs" and should make as contribution to use the park.
He pointed to section 19 of the Local Government Act 1976, which enables local authorities to provide and charge for recreational facilities.
Reacting on the Parkrun Facebook page when the charge was announced, Nick Hayward said: "Absolute disgrace. Parkrun is a great concept that brings all ages, abilities (and pets!) together. Should always be FREE."
Timothy Sowry added: "Unbelievable decision which I hope backfires. Why not try and kill a free inclusive event promoting health wellbeing and community spirit."
Parkrun said the introduction of a charge would mean the end of the Little Stoke event and organisers are finalising plans to move to a new venue.
The final Little Stoke Parkrun will take place later this month.
An MP has accused the government of interfering with plans to charge Parkrun for a weekly event in Bristol.