The United States and Iran agreed to a truce in April but negotiations have stalled and sporadic attacks in the region have continued.
US President Donald Trump issued a new warning to Tehran on Sunday, saying it must move quickly towards a peace deal or "there won't be anything left of them".
The conflict has led to an effective blockade of the Strait of Hormuz, through which around 20 percent of global oil exports pass in peacetime.
The strait "remains meaningfully closed -- now approaching eleven weeks -- after the Trump-Xi summit in Beijing concluded without a breakthrough on reopening the waterway", MUFG's Michael Wan said Monday.
Tokyo shares closed one percent lower and Shanghai lost 0.1 percent, while Hong Kong ended down 1.1 percent.
Sydney, Taipei, Singapore and Wellington also fell, with Jakarta tumbling 3.8 percent.
But Seoul, which has renewed with record highs in recent days thanks to the artificial intelligence spending boom, ended the day 0.3 percent higher.
But government bond yields have risen worldwide in recent trading sessions as more investors start to question if inflation will begin eroding economic growth while pressuring deficits.
"Global government yields rose sharply heading into the start of this week, as three forces collided: surging oil prices, fading hopes for a Strait of Hormuz resolution, and mounting fiscal concerns especially in the UK and US," Wan said.
But last week's talks on trade between China and the United States have offered "a degree of relief for Asian markets", he added.
- 'Wave' of AI demand -
China's consumer spending in April grew at the slowest pace in more than three years, data showed, a stark sign of the challenges Beijing faces to reignite domestic activity.
In Tokyo, shares in memory chip maker Kioxia soared 16 percent following stellar quarterly results on Friday.
Kioxia, the world's third-largest producer of NAND flash memory chips, which are used as storage in AI data centres, has seen its stock surge nearly 300 percent over the past year.
The company has forecast an eye-watering 1.3 trillion yen ($8.2 billion) in operating profit for April-June, saying it is "riding the large wave of AI demand, which has led to record high revenue and profits".
In South Korea, Samsung Electronics, which has also profited massively from the AI memory chip boom, resumed union talks in a bid to avoid a strike over bonus payments.
Samsung shares closed 3.8 percent higher after a court on Monday granted the company an injunction that restricts the scope of the strike, due to begin Thursday, to ensure sufficient staffing levels for safe production and quality control.
Later in the day, traders will have their eye on a meeting of G7 finance ministers and central bank chiefs that kicks off in Paris, with bond selloffs in the spotlight, analysts said.
Then all eyes will be on quarterly results from US chip titan Nvidia, set for Wednesday, which will be scrutinised as investors question whether huge spending on AI data centres is justified by potential returns.
- Key figures at around 0820 GMT -
West Texas Intermediate: UP 2.2 percent at $107.73 a barrel
Brent North Sea Crude: UP 1.7 percent at $111.16 a barrel
Tokyo - Nikkei 225: DOWN 1.0 percent at 60,815.95 (close)
Hong Kong - Hang Seng Index: DOWN 1.1 percent at 25,675.18 (close)
Shanghai - Composite: DOWN 0.1 percent at 4,131.53 (close)
London - FTSE 100: DOWN 0.2 percent at 10,179.06
Pound/dollar: UP at $1.3355 from $1.3316 on Friday
Euro/pound: DOWN at 87.12 pence from 87.25 pence
Euro/dollar: UP at $1.1635 from $1.1620
Dollar/yen: UP at 158.90 yen from 158.78 yen
New York - DOW: DOWN 1.1 percent at 49,526.17 points (close)
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