Boris Johnson has admitted there will be some customs checks for goods after Brexit if they are destined for the Republic of Ireland.

Speaking on Sunday, the prime minister also contradicted claims made by official government papers and his Brexit secretary, and continued to insist there will no checks between goods flowing between Northern Ireland and Great Britain.

It comes after Jeremy Corbyn brandished leaked government papers on Friday showing a Treasury analysis of the prime minister’s proposed Brexit deal. The Labour leader said it offered “cold, hard evidence” the prime minister was misleading the public.

The document, entitled NI Protocol: Unfettered Access to the UK Internal Market, warned the withdrawal agreement has the “potential to separate Northern Ireland in practice from whole swathes of the UK’s internal market”.

The paper added: “At minimum exit summary declarations will be required when goods are exported from Northern Ireland to Great Britain in order to meet EU obligations.”

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Mr Johnson dismissed the Treasury document, but did admit there would be checks on goods that are crossing the Irish Sea and destined for the Republic of Ireland, which will remain an EU member state after Brexit.

Pressed on the details of his Brexit deal on Sky News’s Sophy Ridge on Sunday programme, he said: “Unlike the previous arrangements, it allows the whole of the UK to come out of the EU, including Northern Ireland, and the only checks would be if something was coming from GB via Northern Ireland and was going on to the republic.”

When quizzed on whether there would be some checks both ways between Great Britain and Northern Ireland – a claim made by his own cabinet minister Stephen Barclay – Mr Johnson replied: “That’s wrong because there won’t be checks.

“There is no question of there being checks on goods going NI/GB, or GB/NI because they are part of – if you look at what the deal is, we’re part of the same customs territory and it’s very clear that there should be unfettered access between Northern Ireland and the rest of GB.”

Pressed on whether he was “wilfully misleading” people over the details of the Tories’ proposals, he said: “No, the whole of the UK comes out of the EU. We’re a UK government, why would we put checks on goods going from NI to GB or GB to NI? It doesn’t make sense.”