Brent crude - a key benchmark for oil prices internationally - was lower but still trading close to $90 a barrel.
Prices had already risen in expectation of action by Iran, with Brent crude nearing a six-month high last week.
Analysts said the markets would be looking to see how the conflict could affect global supply chains.
Oil price fluctuations can cause ripple effects across the world due to countries being heavily reliant on the commodity, which is used to produce fuels such as petrol and diesel. Fuel and energy prices have been a major driver behind the higher cost of living worldwide in the past couple of years.
When Russia invaded Ukraine in 2022, oil prices soared to $120 a barrel over supply fears as western nations imposed sanctions on Russia, one of the worldʼs major oil exporters. The jump led to not only higher prices at the pumps, but also countless other goods as businesses adjusted their prices to cover higher costs.
Analysts said Israelʼs reaction to the attack would be key for global markets in the days and weeks ahead.
Israeli Defence Minister Yoav Gallant has said the confrontation with Iran is "not over yet".
His comments came after Iran launched drones and missiles towards Israel at the weekend after vowing retaliation for an attack on its consulate in the Syrian capital Damascus on 1 April. Israel has not said it carried out the consulate strike, but is widely believed to have been behind it.
At the end of last week, the price of Brent crude touched $92.18 a barrel, the highest since October, but on Monday it fell back to around $89.50.
The price of gold - often seen as a safe investment at times of uncertainty - also dropped.
After hitting a record high of $2,431.29 an ounce on Friday, gold fell back to $2,332.97 on Monday.
Energy analyst Vandana Hari said the fall in the price of oil meant "clearly, the oil market does not see the need to factor in any additional supply threat at this point".
But Peter McGuire from trading platform XM.com said he expected the energy market to be volatile and predicted that oil prices would surge if Israel responded strongly to Iranʼs move.
However, April LaRusse, head of investment at Insight Investment, said it was likely that markets would "trade sideways until we have more information".
"Unfortunately this situation in the Middle East has been going on for some time and the longer you have a bit of geo-political tension going on the more markets wait to see and there isnʼt sort of a panic reaction as the first move," she told the BBCʼs Today programme.
Share markets in the Asia-Pacific region slipped on Monday as investors weighed the impact of the attack. The UKʼs FTSE 100 share index also fell marginally.
Russ Mould, investment director at investment firm AJ Bell, said the markets had "started the week with relative calm".
However, he said there was a "continuing nervousness among investors".
"The situation remains fraught and, beyond the geopolitical and humanitarian implications, a more widespread conflict in the Middle East could see energy prices surge and unpick central banksʼ careful efforts to bring down inflation," he added.
Iran is the seventh largest oil producer in the world, according to the US Energy Information Administration, and the third-largest member of the Opec oil producersʼ cartel.
Analysts say that a key issue for the oil price going forward is whether shipping through the Strait of Hormuz will be affected.
The Strait - which is between Oman and Iran - is a crucial shipping route, as about 20% of the worldʼs total oil supply passes through it.
Opec members Saudi Arabia, Iran, the UAE, Kuwait and Iraq send most of the oil they export through the Strait.