Rubio told reporters in New Delhi the US would give diplomacy every chance to succeed before exploring "alternatives", after President Donald Trump said on Sunday he had told his representatives not to rush into any Iran deal.
There was a "pretty solid thing on the table in terms of their ability to open up the strait, get the strait open, enter into a very real, significant, time-limited negotiation on the nuclear matter, and hopefully we can pull it off," Rubio said.
A day earlier, Trump wrote on Truth Social that the US blockade on Iranian ships in the Strait of Hormuz would "remain in full force and effect until an agreement is reached, certified, and signed".
"Both sides must take their time and get it right," he added.
There was no immediate response from Iran's government. But the Tasnim news agency, linked to Iran's Revolutionary Guards, said the US was still obstructing parts of a potential deal, including Tehran's demand for the release of frozen funds.
During military conflict Iran's tactic was "an eye for an eye", and in diplomatic conflict it is "action for action", Ebrahim Rezaei, the spokesperson of the Iranian parliament, said on Monday.
Iran would not yield to pressure or threats, and if the United States wanted an agreement it should negotiate, but if it wanted $6-gasoline it could continue bluffing, he added on X.
Oil prices fell 6 per cent to two-week lows as optimism grew that the United States and Iran were moving closer to a peace deal.
Trump raised expectations of an imminent deal on Saturday when he said Washington and Tehran had "largely negotiated" a memorandum of understanding on a peace agreement that would reopen the Strait of Hormuz.
Before the conflict, the critical waterway had carried a fifth of global shipments of oil and liquefied natural gas.
The two sides remain at odds on several difficult issues, such as Iran's nuclear ambitions, Israel's war in Lebanon with the Iranian-backed Hezbollah militia and Tehran's demands for the lifting of sanctions and the release of tens of billions of dollars of Iranian oil revenues frozen in foreign banks.
A senior Trump administration official outlined what he said were the latest contours of issues being negotiated.
Speaking on the condition of anonymity, the official said Iran had agreed "in principle" to open the Strait of Hormuz, in exchange for the United States lifting its naval blockade, and to dispose of Tehran's highly enriched uranium.
The US understood Iran's Supreme Leader Ayatollah Mojtaba Khamenei had endorsed the broad template of the deal, he added.
There was no immediate confirmation from Iran or elaboration on what an "in principle" agreement meant.
The US official said Washington envisioned first re-opening the strait and lifting the US naval blockade. Negotiating the details of the nuclear measures would take more time.
Iran has long denied US and Israeli accusations that it is pursuing nuclear weapons and says it has a right to enrich uranium for civilian purposes, although the purity it has achieved far exceeds that needed for power generation.
Trump, whose approval rating have been hit by the war's impact on US energy prices, and who has faced congressional efforts to curb his war powers, has repeatedly played up the prospect of a deal to end the conflict started by the US and Israel on February 28.
A tenuous ceasefire has held since early April.
Any deal reinforcing the current fragile ceasefire would bring relief to markets but not immediately defuse a global energy crisis, which has driven up costs of fuel, fertiliser and food.
The US-Israeli bombing of Iran killed thousands of people in Iran before it was suspended in early April.
Israel has also killed thousands more and driven hundreds of thousands from their homes in Lebanon, which it invaded in pursuit of militant group Hezbollah.
Iranian strikes on Israel and neighbouring Gulf states have killed dozens.
