The minister, who said he was considering running for the leadership of the Conservative party following the resignation of Prime Minister David Cameron, insisted that Britain must maintain access to the EU's free-trade zone, but that a deal needed to be struck to limit the free movement of people.
Free trade "is not just at the heart of our economic success -- it is also at the heart of our identity as one of the most open, liberal, outward-looking societies anywhere," he wrote in the Daily Telegraph.
The minister called for a "Norway plus" option, comprising "full access to the single market with a sensible compromise on free movement rules".
This could then be put it to the British public, via a referendum or in the Conservative Party's manifesto ahead of a general election, he said.
Prominent Brexit campaigner Nigel Farage responded that another poll "would be a betrayal" of voters.
The minister also asked other potential Conservative leaders to pledge that full permanent residence be granted to all European citizens living in Britain on the day of the referendum in order to reassure EU citizens concerned about "disgusting examples of anti-Polish xenophobia" seen after Thursday's vote.