Oil price today: Oil prices extended their rally on Tuesday as uncertainty over the Middle East conflict continued to intensify, with the ceasefire proposal now hanging on “life support.” Brent crude futures were up 30 cents, or 0.29%, at $104.51 a barrel, while US West Texas Intermediate rose 31 cents, or 0.32%, to $98.38 at 0002 GMT. Both benchmarks had already surged nearly 2.8% in the previous session on Monday.The gains came as tensions over the ongoing conflict and stalled diplomatic engagement continued to unsettle markets. US President Donald Trump said that the ceasefire with Iran was “on life support.”He also strongly criticised Tehran’s response to a US proposal, saying, “I would call it the weakest right now, after reading that piece of garbage they sent us. I didn’t even finish reading it”, Reuters reported.The latest US proposal had been aimed at restarting talks, but Iran’s reply focused on broader regional demands, including an end to hostilities across multiple fronts such as in Lebanon, where Israel continues its conflict with Hezbollah.Iran’s response also included calls for the lifting of sanctions, guarantees against future attacks, removal of a US naval blockade, compensation for war damage, resumption of Iranian oil sales, and recognition of its sovereignty over the Strait of Hormuz.Tehran, however, later stated that these were not concessions but “legitimate rights”, while accusing Washington of pursuing what it described as a “one-sided approach”.Now, the crucial oil passage of Strait of Hormuz remains a key flashpoint, with Iran asserting control over the waterway that handles roughly a fifth of global oil and liquefied natural gas flows.After the US and Iran launched joint strikes on Iran on February 28, Tehran retaliated by squeezing the Strait of Hormuz. The narrow waterway, through which around 20% of the world’s oil supplies pass, has sent shockwaves through economies as global energy supplies come under strain.