Boris Johnson said "Project Fear is over" after the Chancellor George Osborne said an emergency budget was unlikely to happen until David Cameron's successor takes over in the autumn.
The leading Leave campaigner welcomed Mr Osborne's statement on Monday morning that the UK economy was "about as strong as it could be", as the chancellor tried to calm fears in the markets about the economy post Brexit.
"It is clear now that Project Fear is over, there is not going to be an emergency budget, people's pensions are safe, the pound is stable, the markets are stable, I think that's all very good," Mr Johnson told reporters as he left his London home.
The former Mayor of London also said EU citizens currently living in the UK and British expats living on the continent "have their rights protected", as he sought to clear up "confusion" over their "status".
The FTSE-100 index was down 60.01 points to 6078.68 at 9.15am, as RBS, Barclays and Lloyds suffered falls in their share value.
ITV News Business Editor Joel Hills has the latest:
Look past headline FTSE100 number. UK bank shares RBS -12%, Barclays -9.5%, Lloyds -9% following downgrade by - erm - Barclays analysts.
Joe Trundle, Head of Trading at ETX Capital, said: "Banks are being hammered as a result of Britain’s decision to leave the EU. Aside from the general investor uncertainty, there are some important reasons why financial stocks are so exposed.
"First, there is a realisation that interest rates will remain low for longer – gilts have sunk below 1% for their first time ever today. This is not confined to the UK - Australia’s central bank may have to cut rates because of the vote.
"Second, property assets will have to be revalued and that could severely dent banks’ loan books.
"Thirdly, British banks probably won’t have access to EU markets post-Brexit as they’ll lose their 'passporting' privileges.
The FTSE 100 has fallen 0.82% at the opening of trading on Monday, as the fallout from the Brexit vote continues to hit stock markets.
George Osborne said he would clarify whether he would run for leadership of the Conservative Party this week.
Speaking at a news conference in London on Monday morning, the Chancellor said: "There have been questions about the future of the Conservative Party and I will address my role within that in the coming days."
The Chancellor has said it is "perfectly sensible" to wait until there is a new prime minister before implementing an emergency budget.
Responding to a question by ITV News Business Editor Joel Hills about his earlier statement that Brexit would demand "an immediate response from government," George Osborne said that a financial contingency plan was in place and liquidity had been made available, but an emergency budget would be put in place in Autumn.
The Chancellor George Osborne has said the UK economy is "about as strong as it could be", as he looked to calm market fears following Brexit.
Speaking as financial trading started on Monday, Mr Osborne said the Leave vote in last week's EU referendum was "not the outcome I wanted" but said he "will do everything" he can to "make it work for Britain".
He added that "there will be an adjustment in our economy because of the decision that the British people have taken" but made no indication that there would be an emergency budget.
No sign of the emergency budget that the Chancellor said would be immediately necessary in the event of a Leave vote.
"I respect that decision and we're going to get on and deliver on that decision. But the impact on the economy will have an article on our public finances," he said.
His comments came after the pound suffered fresh losses during early trading on Asian markets on Monday morning.
Addressing the question of the free movement of labour following withdrawal from the EU, the chancellor said Britain is an "open and tolerant country" and he "will fight to keep it so".
The pound suffered fresh losses during early trading on Asian markets on Monday morning.
Sterling was quoted at $1.34 on Monday, down on Friday's close, when it dropped by more than 8% following the referendum result and slipped
Elsewhere, International Monetary Fund Managing Director Christine Lagarde said financial markets "vastly underestimated" the outcome of the vote.
But she added: "There was no panic and the central bankers did the job that they were prepared to do just in case, which was to put a lot of liquidity on the markets."
Chancellor George Osborne will seek to reassure financial markets on Monday morning following Britain's decision to leave the EU.Read the full story ›
Britain is headed for a "mild" recession, Nigel Farage has said - but denied it had anything to do with the UK's vote to leave the EU.
The pound plummeted to its lowest level in 35 years in the immediate aftermath of the referendum result, while stock exchanges around the world suffered a slump in prices as traders panicked in the face of economic uncertainty.
But the Ukip leader, who campaigned for some 25 years for Britain to withdraw from the bloc, told the Sunday Telegraph he believed that would have happened anyway.
"There's nothing new here," he said.
"I think we are going into a mild recession anyway, completely regardless of Brexit. Our growth forecasts are down. Our public-sector borrowing is still not under control at all and everyone forgets that sterling is in a bear market, declining since July 2014."
"Increased global opportunities" await outside the single market, he added, with "no reason" why Britain would not be reaping the benefits within two years.