"The people of the UK have exercised the sacred right of all free peoples. They have declared their independence from the European Union and have voted to reassert control over their own politics, borders and economy," said Trump, who is currently in Scotland on a business trip.
"Come November, the American people will have the chance to re-declare their independence. Americans will have a chance to vote for trade, immigration and foreign policies that put our citizens first," Trump said, seeking to take a political advantage of the British referendum.
In a separate statement, Clinton said she respects the choice the people of the United Kingdom have made.
"Our first task has to be to make sure that the economic uncertainty created by these events does not hurt working families here in America. We also have to make clear America's steadfast commitment to the special relationship with Britain and the transatlantic alliance with Europe," Clinton said.
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"It also underscores the need for us to pull together to solve our challenges as a country, not tear each other down."
Paul Ryan, Speaker of the US House of Representatives, said he respect the decision made by the people of the UK.
"The UK is an indispensable ally of the US, and that special relationship is unaffected by this vote," he said.
"The British people have indicated that they will no longer outsource their future to the EU, and prefer to chart their own path forward," he said.
"The US can learn from the referendum and attend to the issues of security, immigration and economic autonomy that drove this historic vote," Cruz said.
"America will continue to stand with the UK as the British government decides what is the best path going forward. We will continue to deepen and hopefully strengthen our trade and security bonds," said Senator Marco Rubio, the former Republican presidential candidate.