Tom Tugendhat made the comments during a meeting with journalist and activist Vahid Beheshti, who is on the 33rd day of a hunger strike camped on the pavement opposite the UK’s Foreign Office.
During Beneshti’s meeting with Mr Tugendhat, the minister expressed concerns for activist’s health.
“I explained to Mr Tugendhat that I remain firm in my position, and my concerns over the IRGC's undermining of our values, safety and security are growing every day,” the activist said later.
“In the end, I asked Mr Tugendhat to pass my message to our Prime Minister, that he must uphold his pledge to proscribe the IRGC, which he made before being elected.
“I assured him that I will continue my hunger strike until the IRGC is officially proscribed by the government."
While ministers have announced several rounds of sanctions against Iran, they have stopped short of recognising the IRGC as a terrorist organisation.
Iranian protester wants the IRGC placed on Britain's terror list - video
Mr Beheshti has said that sanctions are not enough to deter the IRGC from its malign activities at home and abroad.
He said sanctions imposed by the UK’s Conservative government against Iran, including officials within the regime, did not go far enough.
He said the effect of such punitive measures would not be felt in the short-term and therefore would be ineffective in sending a powerful message.
Mr Beheshti said that only proscribing the IRGC as a terrorist entity would make it clear to the regime that Britain would no longer consider it a credible authority and its human rights abuses would not be tolerated.
On Friday, day 30 of his hunger strike, he wrote an open letter to Mr Sunak, pleading with him to meet him to discuss his demand.
He said the “failure” of past British governments to “stand up to the Iranian regime's oppression in Iran and abroad has reached a critical level”.
Born and raised in Borujerd, a city 400km south-west of Tehran, Mr Beheshti migrated to Britain 24 years ago and has since worked as a journalist and human rights activist.
The tipping point, he said, came in February when the TV station Iran International was forced to close its London studios after journalists received death threats from the Iranian regime.