The pound also traded close to more than 3-1/2 year highs against the euro, benefitting from its image as a relative safe haven from the euro zone's debt crisis.
Market players were looking ahead to UK inflation data for June at 0830 GMT, expected to show prices holding broadly steady from the previous month.
But analysts said sterling/dollar, also known as cable, would take more direction from Fed Chairman Ben Bernanke's testimony to Congress on Tuesday and Wednesday that will be scrunitised for any hints another round of so-called quantitative easing is on its way.
"Sterling is holding up well because now attention has turned to the Fed and QE," said Jane Foley, senior currency strategist at Rabobank.
"There's a risk if Bernanke is not as dovish as some people expect we will see cable lower again, but it seems for the first few hours of today sterling should do well irrespective of the CPI data."
Sterling climbed to a session high of $1.5677, its highest level since July 4, before paring gains to last trade up 0.1 percent at $1.5654.
The euro was steady against the pound at 78.48 pence, not far off Monday's trough of 78.32 pence which was its lowest since late October 2008.
Sterling shrugged off the International Monetary Fund's cut in UK growth forecasts on Monday and has made steady gains versus the euro since the European Central Bank cut interest rates at a policy meeting earlier this month.
Many analysts said although sterling could fluctuate against the dollar it was likely to gain further versus the euro.
"Sterling/dollar looks likely to be dependant on sentiment towards US growth and sentiment towards the euro. But euro/sterling looks likely to continue lower as the medium-term downtrend remains intact," said Lloyds analysts in a note.
Market players may also pay close attention to Bank of England governor Mervyn King's appearance in front of a Treasury Select Committee at 0900 GMT.
Questions are expected to be asked about King's role in the resignation of former Barclays' chief executive Bob Diamond in the Libor scandal, although strategists said that was unlikely to impact the pound.