Under Russia's proposition, regular folks would be permitted to leave, assuming the city's protectors set down arms.
Yet, Ukraine has denied, saying there was no doubt of it giving up the essential port city.
Around 300,000 individuals are accepted to be caught there with provisions running out and help hindered from entering.
Inhabitants have gotten through long stretches of Russian barrage with no power or running water.
Subtleties of the Russian proposition were spread out on Sunday by Gen Mikhail Mizintsev, who said Ukraine had until 05:00 Moscow time (02:00 GMT) on Monday morning to acknowledge its terms.
Under the plans, Russian soldiers would have opened safe hallways out of Mariupol from 10:00 Moscow time (07:00 GMT), at first for Ukrainian soldiers and "unfamiliar hired fighters" to incapacitate and leave the city.
Following two hours, Russian powers say they would then have permitted helpful guards with food, medication and different supplies to enter the city securely, when the defining of the streets was finished.
Russian Gen Mizintsev conceded that a horrendous compassionate disaster was unfurling there - and said the deal would have permitted regular people to escape securely to either the east or west.
Because of the deal, Ukraine's Deputy Prime Minister Iryna Vereshchuk said Ukraine wouldn't quit protecting Mariupol.
"There can be no doubt of any acquiescence, setting down of arms," she was cited by Ukraine Pravda as saying.
Prior to Sunday, Pyotr Andryushenko, who is a consultant to the chairman of Mariupol, promised the city's safeguards would battle on.
"We will battle until the remainder of our troopers," he said.
He told the BBC's News hour that Moscow's philanthropic guarantees couldn't be relied upon, and rehashed unverified cases made by Mariupol authorities lately that Russian powers have been persuasively clearing a portion of its inhabitants to Russia.
"When they [Russian forces] say about compassionate hallways, what do they truly do? They truly force empty our kin to Russia," Andryushenko said.
The BBC has not had the option to confirm these allegations.
Mariupol is a vital key objective for Russia and has seen a portion of the intrusion's deadliest battling.
Russian soldiers have encompassed the city throughout recent weeks, catching its inhabitants inside without admittance to power, water or gas.
Correspondence with regular citizens incapable to leave is restricted yet food and clinical supplies are accepted to be running out and Russia has hindered any philanthropic guide from getting in.
Since the attack started, the port city has seen the absolute generally extreme battling in all of Ukraine, with Russian powers up until this point neglecting to take the city from its safeguards.
As indicated by one gauge, 90% of the city's structures have been harmed or annihilated in assaults since the conflict started three weeks prior, and specialists say something like 2,500 individuals have been killed, albeit the genuine figure might be higher.
After last week's annihilation of a theater where in excess of 1,000 individuals were protecting, on Sunday experts in Mariupol said that an expressions school with 400 individuals inside has additionally been gone after.
Past endeavors to empty Mariupol's regular people have been obstructed by Russian fire, albeit nearby specialists say that thousands have had the option to leave in private vehicles.
On Sunday, the Ukrainian appointee state leader said 3,985 individuals had escaped from Mariupol to Zaporizhzhia, including that Monday the public authority anticipates sending around 50 transports to get further evacuees from the city.
President Volodymyr Zelensky has said the Russian attack adds up to an "atrocity".
"This is an absolutely intentional strategy," he said. "They [Russian forces] have an unmistakable request to do, without question, everything to make the compassionate calamity in Ukrainian urban communities an 'contention' for Ukrainians to help out the occupiers".
The area of the port city, on the Sea of Azov, makes it an essential objective for Russia, as it would assist it with making a land passage between the eastern districts of Donetsk and Luhansk, constrained by Russian-upheld separatists.
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