Investors appear likely to focus on the fallout from another deadly terrorist attack in Britain ahead of an election there on Thursday.
Analysts say British Prime Minister Theresa May needs to win a large majority at the June 8 poll, to give her clout at formal Brexit talks set to begin later this month.
But opinion polls show a much tighter contest than expected - and the impact of the London attacks remains to be seen.
"Markets have been fairly buoyant in recent weeks, but activity is still patchy," KGI Securities (Singapore) trading strategist Nicholas Teo told The Straits Times.
"People are still looking for the next catalyst - especially with earnings season more or less over - and this is likely to come from outside Singapore, he said, pointing to the election, adding that the next interest rate hike in the United States continues to be closely watched.
US data out on Friday showed that jobs growth slowed in May. This could keep a cap on sentiment, though Wall Street shrugged off the weak result to rise 0.29 per cent last Friday.
Still, Mr Michael Feroli, an economist at JPMorgan in New York, told Reuters: "While the message was a little muddied (on Friday), the evidence generally suggests the labour market is cyclically tightening, and the Fed will need to continue to lean against that."
Japan will release first-quarter gross domestic product figures on Thursday, and China will put out data on trade balance and inflation for May on Friday.
Last week, the Straits Times Index chalked up a gain of 20.59 points, or 0.64 per cent, after climbing 4.05 points, or 0.13 per cent, to 3,240.01 on Friday, albeit on sluggish volumes.
One market highlight was news that OCBC Bank and Great Eastern have received proposals from several parties on their combined stakes in United Engineers and WBL Corporation.
Property group United Engineers rose 2.5 per cent, or seven cents, to $2.83 last Friday, while Perennial Real Estate Holdings, which confirmed its interest in United Engineers, advanced 1.1 per cent, or one cent, to 91 cents.
With reporting season at its end, CIMB analyst Lim Siew Khee said that the worst could be over for corporates here, after two years of earnings contraction.
The brokerage is seeing decent upgrades on forward earnings for the first time since the second quarter of 2014 on the stocks it covers, and expects more such upgrades ahead. These will come mainly from the banks, on lower credit costs with the exodus of small-cap oil and gas names; the manufacturing sector, if volume growth is sustained by global demand; as well as consumer stocks, led by sales recovery, said Ms Lim.