Sterling last traded at $1.2756, edging up 0.1 percent on the day, after sliding 1.7 percent on Friday, its biggest one-day drop in around eight months.
The pound had tumbled by as much as 2.5 percent in the previous session to its lowest since mid-April after no single party won a clear claim to power in the UK election on Thursday - a result flagged by some analysts as the worst possible election outcome due to uncertainty.
May is now trying to unite a disillusioned party around her to not only support her in the Brexit talks but also to strike a deal with a small Northern Irish party that will enable her to stay in power.
"There is still heightened uncertainty surrounding issues, including how the (British government's) stance toward Brexit talks might change," said Shinichiro Kadota, senior FX strategist for Barclays in Tokyo.
"The lack of moves (in sterling) is more because the market is waiting for fresh information, rather than a sign that it is settling down," he added.
Negotiations on Britain's exit from the European Union are due to start next Monday.
While sterling has retreated as investors with long positions moved back towards neutral, there is no reason to expect further weakness simply because of the election result, said Andrew Milligan, Edinburgh-based head of global strategy for Standard Life Investments.
"On valuation grounds, sterling is about fair value versus the other major currencies, so to see a much cheaper currency would require considerable new news on either the state of the UK economy or on the state of Brexit negotiations."
Milligan added that it is "far too soon" to say how the election results may affect the Brexit talks.
The euro edged up 0.1 percent to $1.1208, staying below a seven-month high of $1.1285 set in early June.
The euro showed little reaction, after projections following the first round of French parliamentary elections on Sunday showed that President Emmanuel Macron's fledgling party was set to secure a huge majority. The outcome of initial results was in line with expectations.
The dollar held steady at 110.29 yen, having retreated from Friday's one-week high of 110.815 yen.
Analysts said the dollar could come under pressure against the yen, if falls in U.S. technology shares deepen after the sell-off seen on Friday, when the Nasdaq Composite tumbled 1.8 percent.
"If it spills over into broader (U.S.) stock indices, that could trigger risk-off moves and put downward pressure on the dollar against the yen," said Hirofumi Suzuki, economist for Sumitomo Mitsui Banking Corporation in Singapore.
A key focus for markets this week is the Federal Reserve's two-day policy meeting that ends on Wednesday.
With the Fed widely expected to raise interest rates, investors' focus will be on any fresh hints on the pace of further tightening in the months to come and next year, and any further details on its plans for trimming its balance sheet.