Bob Seely, who sits on the Commons foreign affairs committee, said the move would provide better integration between departments and see in a greater “coherence” in the approach to foreign affairs.
The Conservative MP said Mr Hunt’s office should take control over Department for International Trade (DIT), Department for International Development (DFID), defence, the Cabinet Office and even Prime Minister Theresa May’s office.
Mr Seely made the comments in the Commons as MPs debated a post-Brexit “global Britain”.
He said: “Global Britain is a great phrase but we really need to fill it out, there are some questions I have about it.
“What are we prioritising, every time our foreign affairs committee says ‘what are you prioritising’, it’s everything.
“The FCO (Foreign and Commonwealth Office) doesn’t have unlimited resources, global Britain is more than just opening half a dozen extra posts in Papua New Guinea, it has to amount to something.
“I am quite a fan of the argument to suggest that the FCO should be a super ministry and having an oversight, a stronger role leading DIT and DFID and defence and the Cabinet Office and the Prime Minister’s office.
“There are so many bits of Government which are now involved in foreign affairs, we want coherence and above all I think the critical thing that we need to learn is how we integrate government better.”
Mr Seely also urged ministers to adopt a number of new measures to combat Russian aggression.
He demanded a “small, permanent multi-agency group” whose role would be to understand and expose foreign subversive activities, both here and abroad, that threaten the UK’s interests.
He added: “Second, we need to introduce a list of PR agencies, reputation management firms and others who work as agents for Russian influence in the UK.
“If you want to work for Putin or his cronies, directly or via their proxies, you need to be open about it.”
Russian nationals have been named as suspects in the March novichok poisoning of former spy Sergei Skripal and daughter Yulia, who were found slumped on a park bench in Salisbury, Wiltshire.
Police named Alexander Petrov and Ruslan Boshirov as suspects yesterday.
The Kremlin has continued to deny any involvement in the attack.