His remarks came after the Foreign Office said it was "almost certain" that a branch of the Iranian military - the Islamic Revolutionary Guard Corps - attacked the two tankers in the Gulf of Oman earlier this week.
"No other state or non-state actor could plausibly have been responsible," a government assessment of the situation added.
Donald Trump claimed on Friday the oil tanker attack had "Iran written all over it", as the the US military released footage it said showed an unexploded mine being removed from one of the tankers by Iranian special forces.
Iranian president Hassan Rouhani hit back accusing Washington of "carrying out an aggressive policy and posing a serious threat to regional stability", as his ministers claimed the US had made allegations "without a shred of factual or circumstantial evidence".
But on his social media account, Mr Corbyn, the Labour leader, said: "Britain should act to ease tensions in the Gulf, not fuel a military escalation that began with US withdrawal from the Iran nuclear agreement.
"Without credible evidence about the tankers attacks, the government's rhetoric will only increase the threat of war."
Shadow foreign secretary Emily Thornberry later added on BBC's Radio 4 Today programme that it was important to establish independent evidence - a call made by the UN secretary general Ańtonio Guterres.
"The idea that we are going to get enmeshed in another war is something that we really need to think about very carefully," she said.
But Mr Corbyn was quickly rounded on by his critics, with the foreign secretary Jeremy Hunt characterising the Labour leader's response as "pathetic and predictable".
"From Salisbury to the Middle East, why can he never bring himself to bak British allies, British intelligence of British interests?"
Dominic Raab, who is vying to succeed Theresa May as Britain's next prime minister alongside Mr Hunt, added: "Yet again Jeremy Corbyn allows his anti-American prejudice to skew his moral compass and political judgement."
In a statement released on Friday, Mr Hunt added: “I condemn yesterday’s attacks on two vessels in the Gulf of Oman. Our own assessment leads us to conclude that responsibility for the attacks almost certainly lies with Iran. These latest attacks build on a pattern of destabilising Iranian behaviour and pose a serious danger to the region."