Donald Trump said on Saturday he was going to review a new peace proposal from Tehran but cast doubt over its prospects, saying Iran had not yet “paid a big enough price”.

Two semiofficial Iranian news outlets, Tasnim and Fars, believed to be close to Iran’s paramilitary Revolutionary Guard, said Iran had sent the US a new 14-point proposal via Pakistan.

“I’ll let you know about it later,” Trump said of the proposal on Saturday, before boarding Air Force One, adding that “they’re going to give me the exact wording now”.

Shortly after speaking to reporters, Trump posted on social media about the new proposal, saying he “can’t imagine that it would be acceptable in that they have not yet paid a big enough price for what they have done to Humanity, and the World, over the last 47 years.”

Trump rejected a previous Iranian proposal this week. However a ceasefire in the war – launched by the United States and Israel in late February – has been in effect since 8 April, with one failed round of peace talks having taken place in Pakistan.

Iran’s deputy foreign minister Kazem Gharibabadi told diplomats in Tehran “the ball is in the United States’ court to choose the path of diplomacy or the continuation of a confrontational approach”.

Iran, he said, was “prepared for both paths”.

Washington has repeatedly said it will not end the war without a deal that prevents Iran from obtaining a nuclear weapon, the primary aim Trump cited when he launched strikes in February in the midst of nuclear talks. Iran says its nuclear program is peaceful.

Reuters and other news organisations have reported over the past week that Tehran is proposing to reopen the strait before nuclear issues are resolved.

Iranian media said Tehran’s latest 14-point proposal included the withdrawal of US forces from areas surrounding Iran, lifting the US blockade on the strait of Hormuz, releasing Iran’s frozen assets, payment of compensation, lifting sanctions and ending the war on all fronts, including Lebanon, as well as a new control mechanism for the strait.

Speaking to reporters in Florida on Saturday, Trump suggested new military action against Iran was on the table.

“If they misbehave, if they do something bad, but right now, we’ll see,” he said. “But it’s a possibility that could happen, certainly.”

Elsewhere, the US warned shipping companies they could face sanctions for paying Iran to pass safely through the strait of Hormuz, adding pressure in the standoff over control of it.

Iran has maintained a stranglehold on the strait since the war began, choking major flows of oil, gas and fertiliser to the world economy. The US has responded with a naval blockade of Iranian ports, depriving Tehran of oil revenue it needs to shore up its ailing economy.

Oil prices are about 50% above prewar levels.

The US on Friday warned against payments to Iran, not only in cash but also in “digital assets, offsets, informal swaps, or other in-kind payments,” including charitable donations and payments at Iranian embassies.

With Reuters, the Associated Press and Agence France-Presse