Polish-born Daniel Kawczynski has been lobbying the government in Warsaw to reject the request.
Under the terms of Article 50, the clause that sets out the rules for the process of a country leaving the bloc, all 27 remaining EU states need to agree the delay for it to be granted.
In a tweet on Sunday, Mr Kawczynski said he was doing “all I can” to convince Poland to vetos delay and “others [are] working on Czechs and Hungarians”.
Speaking to Sky’s All Out Politics, the MP for Shrewsbury and Atcham defended his move.
He said: “It is our job to do anything that is legal and constitutional to ensure that we leave the European Union on 31 October.
“We have a hardcore Remainer parliament and Remainer MPs that are trying to block and thwart the will of the British people.
“So of course we have to take whatever actions we need to.”
He added: “The problem we have is that the EU acts as a mafia cartel and any country is frightened of putting their head above the parapet and being the one country that says there shouldn’t be an extension.
“So we’re hoping that Warsaw and Budapest combined might have the courage to actually do this.”
Mr Kawczynski previously tried to stop the first delay to Brexit earlier this year, when Theresa May was prime minister.
He came in for criticism for the move, with Labour MP David Lammy saying it was “extraordinarily reckless”.
Prime Minister Boris Johnson asked for a three-month delay to Brexit on Saturday.
The request came hours after MPs voted to withhold approval for his Brexit deal unless and until he has passed all of the legislation to implement it.
Mr Johnson was legally required to request this delay under the so-called “Benn Act”.
This is the legislation passed by opposition MPs in September to prevent a no-deal Brexit at the end of this month.