The feared troops, armed with machine guns and rocket launchers, have been used as a PR tool in Putin's war, and photos of them in the city suggest the dictator believes he is on the verge of taking it.
Propaganda channels have previously pumped out pictures and videos of the notorious fighters in conquered territories to boost Russian morale.
Some Chechen soldiers are fighting alongside the Russian military, which waged two wars against Chechnya – a Muslim republic in southern Russia – between 1994 and 2000.
Among the Chechen fighters pictured in Mariupol was the regiment commander Zamid Chalaev, who is accused of human rights violations.
Thanks to fierce Ukrainian resistance, Mariupol has held out for over a month despite Russia's brutal bombardment.
But Russia finally entered the city centre this week and some observers believe its fall is imminent.
It comes as the invading forces were accused of looting 14 tons of humanitarian aid destined for the southern port – and a convoy of 45 buses bringing medical supplies was allegedly blocked from entering on Thursday night.
Ukrainian soldiers on Friday liberated the suburban town of Irpin and the Hostomel air base on the outskirts of Kyiv while also regaining control of the heavily contaminated Chernobyl nuclear site early on Friday morning.
The exchange of control happened amid growing indications the Kremlin is using talk of de-escalation in Ukraine as cover to regroup, resupply its forces and redeploy them for a stepped-up offensive in the eastern part of the country.
The Russian military in the northeast continued to block and shell Chernihiv and Kharkiv on Friday and Ukraine's general staff said its forces were bracing for an all-out assault in the country's east.
In the southeast of the country the Russians are trying to seize the cities of Popasna, Rubizhne and Mariupol in order to expand the territory of separatist republics of Donetsk and Luhansk, according to the Ukrainian military.
Russian troops left the heavily contaminated Chernobyl nuclear site early on Friday morning after returning control to the Ukrainians, authorities said.
Ukraine's state power company, Energoatom, said the pullout at Chernobyl came after soldiers received 'significant doses' of radiation from digging trenches in the forest in the exclusion zone around the closed plant.
But there was no independent confirmation of that.
Announcing the exchange on Friday, Ukrainian Foreign Minister Dmytro Kuleba said the Russians behaved irresponsibly at the site during the more than four weeks that they controlled it, preventing staff at the plant from performing their full duties and digging trenches in contaminated areas.
Kuleba told a news conference in Warsaw that the Russian government had exposed its soldiers to radiation, endangering their health.
Russia said during negotiations on Tuesday that it would scale down operations in the Kyiv and Chernihiv regions.
Fighting has continued in both regions and NATO Secretary-General Jens Stoltenberg has said Russian forces are not withdrawing but regrouping.
'We are observing the movement of joint (Russian) vehicle columns of various quantities,' the Kyiv region's governor, Oleksandr Pavlyuk, wrote on the Telegram messaging app.
Pavlyuk said some of the troops were heading towards the border with Belarus, a Russian ally.
He said Russian forces had left the village of Hostomel, which is next to an important airport, but were digging in at the town of Bucha.
Moscow's men have suffered heavy losses in the five week war and NATO estimates between 7,000 and 15,000 Russian soldiers have been killed in the fighting.
Ukraine claims as many as 17,000 have been killed.
Putin this week ordered 134,500 more conscripts aged 18 to 27 to join his army as part of the annual spring military draft, which runs from April 1 to July 15.