Ann Linde, the Swedish minister for EU affairs and trade, said she was shocked by the uncertainty and xenophobia experienced by Swedes in the UK since the referendum.
Minister Linde said the future of an estimated 100,000 Swedish people in Britain and 30,000 British people in Sweden, had to be urgently dealt with.
She said: “This is one of the very most important issues and we have to solve it in a very constructive way in the first part of the negotiations.”
She was speaking in central London following a meeting with Swedish citizens and ahead of a meeting with David Davis, the Brexit secretary.
The British government has said it would like to guarantee EU citizens the right to live in the UK but it cannot unless the guarantee is reciprocated by the other 27 member states.