The impact of the most recent London attack, however, is likely to have a "very limited" on the markets, JPMorgan Asset Management's Chief Asia Market Strategist Tai Hui told CNBC.
"If you look at various attacks in the past six to nine months in Europe or other parts of the world, their impact or the impression on the market tends to be very limited, if at all," Tai said.
"Obviously, if that does steer towards a change in the political landscape in the U.K. for the election this week ... (in the) next several quarters, obviously that might have a marginal market impact," he added.
The attack over the weekend would mostly have a "minimal" impact on the pound's trajectory, Nomura G10 FX Strategist Peter Dragicevich told CNBC.
"I think the bigger focus is obviously the election on Thursday in the U.K. There is still a lot of uncertainty around which party will win. The polls do still suggest a majority for the Conservatives, but clearly the probability has declined with the narrowing in the polls," Dragicevich said.
The ASX 200 shed 0.57 percent or 33.214 points to close at 5,754.9, driven largely by weakness in major financial stocks.
Markets in China were mixed despite the positive read from the May Caixin services PMI, with the Hang Seng Index down 0.41 percent at 3:00 p.m. HK/SIN. The Shanghai Composite closed 0.45 percent or 14.0138 points down at 3,091.5262 while the Shenzhen Composite finished higher by 0.689 percent or 12.3292 points at 1,800.9325.
The Caixin services PMI came in at 52.8, compared to the 51.5 figure seen last month. This month's services PMI reflected that growth in the sector grew the quickest in four months.
New Zealand markets are closed for a holiday.
Shares of Japanese automakers were mostly lower on the strength of the yen, with Toyota falling 2.04 percent to close at 5,968 yen a stock. The company had announced over the weekend it had sold its shares in Tesla after the end of a partnership to develop electric cars.
"The dollar remains weak, and there will be few catalysts to reverse this until the Federal Open Market Committee (FOMC) meeting next week," Jo Masters, an economist at ANZ, said in a Monday morning note.
The greenback gained slightly against the yen after falling last Friday, with dollar/yen trading at 110.60 yen.
Meanwhile, demand for safe-haven assets rose. Gold traded at its highest levels in around six weeks earlier in the session. Spot gold prices stood at $1,279.22 at 2:30 p.m. HK/SIN.
Stateside, Wall Street closed at record highs after the release of May non-farm payrolls despite job creation coming in at 138,000 compared to the 185,000 forecast.
Banco Popular shares slumped over 18 percent on Monday as the embattled Spanish lender hit the bottom of the benchmark. The bank has been struggling since reports emerged that the bank would have to be wound down if it didn't find a buyer.
Shares of the Portuguese energy firm EDP also fell more than 2 percent on Monday after its CEO was named a suspect in a corruption investigation. The company said it would inform the market with further details about the investigation on Tuesday.
Meanwhile, in the U.S., stocks continued under pressure after a weekend attack in Britain and geopolitical tensions in the Middle East.
U.K. PMI services data also came in lower than expected as a national election has derailed investment decisions and higher inflation has hit households, Reuters reported.
London attacksU.K. Prime Minister Theresa May said that it's time to step up the fight against Islamist extremism in the wake of the new attack. "It is time to say enough is enough," she told the media after a terrorist attack killed at least seven people in central London on Saturday night.
Sterling stabilized after an initial drop on Monday with the country set for an election in four days' time. The Conservative leader has been losing ground to her Labour opponent in the past few weeks. The dollar index hit its lowest level since the November U.S. election on Monday after a jobs report Friday came in lower-than-expected.
Oil prices dipped during afternoon trade on Monday, erasing gains supported by a political rift in the Middle East, before investor concerns over a global supply overhang returned.
Brent crude traded at around $49.21 a barrel on Monday shortly after the European close, down 1.48 percent, while U.S. crude was around $47.08 a barrel, down 1.22 percent.
The S&P 500 slipped 1 percent, with materials and utilities lagging. The Dow Jones industrial average fell about 20 points, with Apple contributing the most losses. The Nasdaq composite traded 0.1 percent lower after reaching an all-time intraday high.
Rob Lutts, chief investment officer at Cabot Wealth Management, said two key elements supporting this market are the relative value of stocks versus other alternatives, like bonds, and strong earnings growth.
"Clearly the market is more expensive compared to a few years ago, but earnings have justified those valuations," he said.
Still, some traders are worried about this stock-market rally as a large chunk of this year's gains have come from just five large-cap tech stocks.
"The averages are making new highs but that's because of a handful of stocks. If you take those out, we'd probably be lower," said Peter Cardillo, chief market economist at First Standard Financial.
Apple's stock fell 1 percent after Pacific Crest analyst Andy Hargreaves downgraded the stock to sector weight from overweight. In a Sunday note, Hargreaves said the stock is not pricing in potential risks, like supply issues with the new iPhone 8.
"We believe AAPL anticipates strong performance in the iPhone 8 cycle, while providing relatively little weight to risks through the cycle or the potential for iPhone sales to decline in FY19," he said.
Investors also kept an eye on Apple's annual developers' conference on Monday, where the revealed several new products.
Stocks traded in a narrow range for most of Monday's session, with the S&P moving just 0.21 percent.
"There's not a lot of economic news to really decipher," said Nick Raich, CEO of The Earnings Scout, noting the market will remain in a "wait-and-see mode for a few weeks until we get peak second-quarter earnings."
In economic news, the IHS Markit U.S. services PMI for May came in at 53.6, up from 53.1 in April, marking "the largest rise in overall activity since February," IHS said in a release.
The May ISM nonmanufacturing index, meanwhile, came in at 56.9, just below a consensus estimate of 57.0.
Overseas, European stocks traded lower as investors digested a terrorist attack in London that killed at least seven people on Saturday night.
The FSTE 100 fell 0.27 percent, while the French CAC 40 dropped 0.66 percent. The pan-European Stoxx 600 index fell 0.1 percent.
U.K. Prime Minister Theresa May said that it's time to step up the fight against Islamist extremism in the wake of the new attack. "It is time to say enough is enough," she said.
The S&P 500 slipped 2.97 points, or 0.12 percent, to end at 2,436.10, with utilities leading seven sectors lower and energy the top advancer.
The Nasdaq declined 10.11 points, or 0.16 percent, to close at 6,295.68.
About nine stocks declined for every five advancers at the New York Stock Exchange, with an exchange volume of 699.47 million and a composite volume of 2.893 billion.
The CBOE Volatility Index (VIX), widely considered the best gauge of fear in the market, traded near 10.1.
—CNBC's Silvia Amaro and John Melloy contributed to this report.
On tap this week:
Earnings: Coupa Software, Thor Industries
Earnings: Dave & Buster's, Lands' End, Michaels Cos, Ambarella, IDT, United Natural Foods, Canadian Solar, Oxford Industries
10:00 a.m. JOLTs
10:00 a.m. QFR
Earnings: Brown-Forman, ABM, Greif, Verint Systems
3:00 p.m. Consumer Credit
Earnings: Dell Technologies, JM Smucker, Vail Resorts, Verifone, Cloudera
7:45 a.m. European Central Bank rate decision
8:30 a.m. News conference with ECB President Mario Draghi
8:30 a.m. Initial claims
10:00 a.m. QSS
Earnings: Ferrellgas Partners
10:00 a.m. Wholesale trade