Following his remarks, sterling trimmed its losses, trading at $1.34441 from $1.3400 before Osborne spoke. The FTSE 100 opened 0.7 percent lower on Monday, a less severe open than expected ahead of the speech.
The Chancellor added that the U.K. faced particular challenges including market volatility "that we have seen and are likely to continue to see" and political uncertainty while the U.K. negotiates a "new relationship" with the rest of Europe.
"It will not be plain sailing in the days ahead but let me be clear, you should not underestimate our resolve," he said, adding that the Treasury and Bank of England had systems in place to dampen any adverse financial shocks.
The referendum's result, which took some markets and pollsters by surprise, sent financial markets in the U.K. and around the world into a tailspin on Friday with sterling falling to a 30 year low.
Prime Minister David Cameron, who campaigned for Britain to remain a part of the bloc, announced his resignation soon after the result but said he would stay on as leader until October in a bid to offer some stability at a time of heightened uncertainty.
Osborne, who made no mention of following Cameron's suit by resigning, had threatened during campaigning an immediate "emergency budget" if there was a Brexit vote. However he seemed to backtrack from that pledge, saying that there would be a delay until a new prime minister was elected later in the year.
""As I said before the referendum, this will have an impact on the economy and the public finances – and there will need to be action to address that," he said, "but I think it is perfectly sensible to wait until we have a new prime minister to address that."
He said that only the U.K. could trigger Article 50 which sets in motion the process of leaving the EU and that it was right to delay doing so until there is a "clear view about what new arrangement we are seeking with our European neighbors."
"Given the delay in triggering Article 50 and the Prime Minister's decision to hand over to a successor, it is sensible that decisions on what that action should consist of should wait for the OBR (Office for Budget Responsibility) to assess the economy in the autumn, and for the new Prime Minister to be in place."
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