Brent crude, the main benchmark for global oil prices, was lower on Monday morning but remained near $90 a barrel.
Prices have risen on expectations of Iran production, with Brent nearing a six-month high in the last week.
Israel's Defense Minister, Yoav Galant, said, "it's not over yet."
"Obviously, the oil market is not taking into account the threat of further supply," said energy analyst Vandana Hari.
Brent crude may fall below the $90 mark, but a sharp correction is unlikely as traders continue to focus on problems related to the conflicts in Gaza and Ukraine, he added.
Analysts also said that Israel's response to the attack will be important to international markets in the coming days and weeks. Peter McGuire of trading platform XM.com told the BBC that he expects energy markets to be volatile and predicts that oil prices will rise if Israel takes a more aggressive stance against Iran.
However, April LaRuse, chief investment officer at Insight Investment, said the market will "trade sideways until the news arrives."
"Unfortunately, this has been happening in the Middle East for some time, and as long as the geopolitical tensions continue, there will be more time for the markets to wait and see, and there will be no sudden reaction. ," he added.
Shares in Asia-Pacific fell on Monday as investors weighed the impact of the attack.
Hong Kong's Hang Seng Index, Japan's Nikkei 225 Index and South Korea's Kospi Index all weakened, while the Shanghai Stock Exchange Composite Index rose more than 1%. Gold prices rose, nearing all-time highs and trading around $2,400 an ounce.
Gold is considered a safe investment in times of uncertainty and will rise significantly towards the end of the week.
Why did Iran attack Israel?
Iran has vowed to retaliate for the April 1 attack on its consulate in the Syrian capital, Damascus, and to fire drones and missiles at Israel during the week.
Israel has not claimed responsibility for the attack on the council, but the conspiracy behind it. At the end of the week, the price of Brent crude reached $92.18 a barrel, the highest since October, before recovering to close at $90.45 on Friday.
Iran is the world's seventh-largest oil producer and the third-largest member of the OPEC oil-producing cartel, according to the US Energy Information Administration.
Analysts said the key question for future oil price trends is whether shipping in the Strait of Hormuz will be disrupted.
The strait connecting Oman and Iran is a major shipping route through which 20% of the world's oil supplies pass.
Most of the oil exported by OPEC members Saudi Arabia, Iran, the United Arab Emirates, Kuwait and Iraq crosses the strait. On Saturday, Iran seized a commercial ship with ties to Israel as it passed through the Strait of Hormuz.