The Justice Secretary argued Britain would be able to negotiate a series of tariff-free trading deals with other European nations if it left the European Union.
Remain campaigners insisted the idea that European nations would allow Britain access to the single market without was fanciful while George Osborne claimed leaving the EU would have a damaging impact on house prices.
The interventions by leading figures in both campaigns marked the resumption of hostilities following the local elections and ahead of the June 23 referendum on Britain’s EU membership.
The Prime Minister will enter the fray again tomorrow with a speech arguing membership is critical to Britain’s economic and national security.
Mr Gove claimed remaining in the EU would mean the country “could lose autonomy economically”.
He said: “We should be outside the single market, we should have access to the single market but we should not be governed by the rules that the European Court of Justice imposes on us which cost business and restrict freedom.”
He added: “At the moment there are no tariffs between the UK and other countries in the European Union. Why should we seek to impose those tariffs when we are outside?”
But his opponents questioned the logic of leaving the single market when Britain wants to enjoy the benefits if offers.
Writing on Twitter, Jurgen Maier, chief executive of Siemens UK which is building a wind turbine plant in Hull, said: “So let me understand this.
“We want to be outside the single market but want to be in it? Sound stupid?”
Mr Osborne claimed Mr Gove’s suggestion amounted to an admission that leaving the EU would mean leaving the single market.
“That would be catastrophic for people’s jobs and their incomes and their livelihoods,” he said.
Mr Osborne said Treasury analysis showed leaving the EU would lead to “a significant shock to the housing market, that would hit the value of people’s homes, that would hit the cost of mortgages.”
The Chancellor also tried to shrug off calls for Mr Cameron to take part in a TV debate with leading Leave campaigner and fellow Conservative Boris Johnson.
Challenged on ITV’s Peston on Sunday over the lack of a debate, Mr Osborne said: “I know everyone wants to turn it into a Tory soap opera but it’s more important than that.”
The Prime Minister will use his speech tomorrow to argue that Britain’s national interest is best served by staying in the EU.
He will say: “If my experience as Prime Minister had taught me that our membership of the EU was holding Britain back or undermining our global influence, I would not hesitate to recommend we should leave.
“But my experience is the opposite.
“The reason I want Britain to stay in a reformed EU is in part because of my experience over the last six years is that it does help make our country better off, safer and stronger.”
Two former UK security service chiefs today argued that Brexit could hamper the UK’s ability to protect against terrorism. They said the UK benefited from the exchange of information with other EU countries.