Sterling was trading at $1.3365, down almost 3% from Friday's close. Against the euro it was trading at €1.2147, down 1.4%.
On Friday the pound had its biggest one-day fall against the dollar, at one stage sinking as low as $1.3236.
George Osborne will issue a statement before the start of trading in the UK in a bid to calm the markets.
The Chancellor has not spoken publicly since the Leave campaign won Thursday's referendum.
Authorities in Asia have been taking action to stabilise financial markets.
(BBC News)