Speaking ahead of a meeting of European finance ministers in Brussels, Mr Hammond said: "We will continue to abide by the rules, and the regulations and the laws, of the European Union for so long as we are members.
"Of course we want to strengthen our trade ties with the very many trade partners we have around the world, but we're very mindful of our obligations under the treaty and we will follow them precisely."
The UK is only allowed to talk about deals with new partners in principle and cannot start negotiations on free trade agreements before we leave the EU.
The Prime Minister told Republicans in the United States last night she was "looking forward to pursuing talks" about a new UK and US free trade agreement.
"It will take detailed work," Mrs May said in a speech in Philadelphia.
"But we welcome your openness to these discussions and hope that we can make progress so the new global Britain that emerges after Brexit is even better equipped to take its place confidently in the world."
European leaders have expressed their consternation this week about Britain embarking on a trade talks before our exit from the EU is finished.
An EU commission spokesman on Tuesday told reporters that if a country wants a divorce but good future relations they must have an orderly transition.