The third round of Brexit negotiations, focused on settling the terms of Britain's exit from the EU, ended on Thursday with a warning from Brussels that more work needed to be done before they moved on to discuss future ties.
The British government has been keen to shift talks to a new relationship, seeking to allay business concerns on trade and regulation, but Brussels has demanded progress first on central issues, including how much Britain should pay when it leaves.
"We can't be blackmailed into paying a price on the first part," Fox told broadcaster ITV during a visit to Japan with Prime Minister Theresa May.
The so-called Brexit bill is a contentious issue both domestically, where eurosceptics are keen to see as little money paid as possible, and with the EU, which is demanding Britain meets its existing commitments to the bloc.
Britain has said it is prepared to meet its international obligations.
Fox said businesses across Europe had told him they were keen to see more detail on what Britain's new relationship with the EU would look like.
"We think we should begin discussions on the final settlement because that's good for business, and it's good for the prosperity both of the British people and of the rest of the people of the European Union," Fox said.
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