Mrs Truss also assured MPs that agricultural standards would not be compromised in a US-UK deal.
A ban on chlorinated chicken was “already in UK law” as part of the Brexit Withdrawal Agreement and monitored by the Food Standards Agency, she said.
However, Mrs Truss twice refused to rule out a “dual-tariff” regime, which would impose lower duties on higher quality goods such as organically reared free-range meat in order to encourage foreign producers to raise their animal welfare to British levels.
US trade representative Robert Lighthizer has said a trade deal with Britain is “almost impossible” before the November presidential elections.
Mrs Truss added that the UK would not be “bounced into a quick deal” with Japan, after Tokyo’s chief negotiator Hiroshi Matsuura, gave Britain only six weeks to strike an arrangement – a blow to the Government, which had hoped to secure deep trade liberalisation with the country.
Ms Truss repeatedly declined to say whether she had been given assurances about the future of her department, after speculation it will be folded into the Foreign and Commonwealth Office (FCO).
She said: “The Prime Minister is very clear that the Department for International Trade (DIT) remains and has a lot of important work to do.”
SNP MP Angus MacNeil, the trade committee’s chairman, asked: “We know it remains, but how long for?”
Mrs Truss said: “What is also clear is that we have to speak with one voice internationally, which is why I’m working very closely with the Foreign Secretary, which is why our trade commissioners are working closely with local ambassadors and high commissioners.”
Asked about the impact of the rumours on staff morale at DIT – as well as talk that Antonia Romeo, its permanent secretary, is being lined up to replace Simon McDonald, the head of the FCO – Ms Truss said her staff are doing a “fantastic job”.
Presented with DIT’s own analysis that the trade deal it seeks to strike with New Zealand could have a negative long-term effect on the UK economy, Ms Truss disputed the value of her department’s forecasts.
She said: “These are scoping studies about a hypothetical deal.”