1. 'Kremlin wants to end the war as soon as possible', claims Erdogan
Turkish President Recep Tayyip Erdogan has claimed that Russia and Ukraine have agreed to exchange 200 prisoners.
Erdogan told PBS that the deal was a "significant" step forward but did not provide any further details about the agreement.
Erdogan, who met Russian President Vladimir Putin last week in Uzbekistan, has said the Kremlin "wants to end the war as soon as possible".
The Turkish president has managed to maintain ties with Moscow and Kyiv since the start of the Russian invasion on February 24.
Ankara has regularly offered to mediate in the conflict "to find a deal that satisfies everyone" and returns Crimea and occupied territories to Ukraine.
Erdogan is due to address the United Nations General Assembly in New York on Tuesday.
2. Ukraine's counteroffensive progresses
Ukraine has claimed that its troops have marched farther east into territory that was recently abandoned by Russia.
"The occupiers are clearly in a panic," Ukrainian President Volodymyr Zelensky said in his nightly televised address on Monday.
"The speed at which our troops are moving. The speed in restoring normal life," he added.
The progress of the counteroffensive means Ukraine could soon launch an assault on Russian forces in the occupied Donbas region.
Ukraine's armed forces had regained complete control of the village of Bilohorivka and were preparing to retake all of Luhansk province from Russian occupiers, according to provincial Governor Serhiy Gaidai said.
Kyiv has begun to push into Luhansk after driving Russian forces out of the northeastern Kharkiv province in a counter-offensive earlier this month.
Ukraine’s southern military command has also reported that its troops sank a Russian barge carrying troops and weapons across the Dnipro River near the Russian-occupied city of Nova Kakhovka.
The Institute for the Study of War said on Tuesday that Ukraine is now deploying captured Russian tanks and artillery to solidify its gains.
“The initial panic of the counteroffensive led Russian troops to abandon higher-quality equipment in working order, rather than the more damaged equipment left behind by Russian forces retreating from Kyiv in April, further indicating the severity of the Russian rout,” the Washington-based think tank said.
3. Number of graves exhumed at Izium increases
In the wake of Ukraine's counteroffensive, Ukrainian officials say they have found hundreds of graves near the city of Izium.
Forensic experts say they have so far exhumed 146 bodies at a mass burial site in a nearby forest. Some of the bodies reportedly bear signs of violence and torture.
President Zelenskyy has said some 450 bodies are believed to have been buried at the site before it was recaptured by Ukrainian forces.
"There are bodies with tied hands and traces of torture, said Oleh Synehubov, governor of the Kharkiv region. The deceased were also found to have explosive, shrapnel and stab wounds," he added on Telegram.
Kremlin spokesman Dmitry Peskov has rejected Ukraine's allegations as a "lie". Russia has repeatedly denied claims of war crimes.
Moscow meanwhile stated that a Ukrainian strike on a village in the Luhansk region on Monday night killed seven civilians, including three children.
4. Russia-installed leaders to hold referendums
The Russian-installed leaders of four regions of southern and eastern Ukraine have reiterated urgent calls for referendums to join Russia.
The appointed governor in Kherson, Vladimir Saldo, said on Telegram that a vote would be held in his region between September 23 and 27.
Similar moves were then announced by Russian-installed leaders in Zaporizhzhia and the two Donbas regions -- Luhansk and Donetsk soon after. It would mean around 15% of Ukrainian territory -- an area about the size of Hungary or Portugal -- would vote on joining Russia.
Denis Pushilin, head of the separatist Donetsk region, had called on his counterpart in Luhansk province to combine efforts aimed at preparing a referendum, stating that "actions should be synchronised".
Plans for referendums have previously been discussed but have been delayed, possibly due to a lack of popular support.
On Tuesday, former Russian President Dmitry Medvedev also said that Russian-backed referendums were "essential" to protect the regions' interests and allow Moscow to increase its military force in the Donbas.
"Encroachment onto the territory of Russia is a crime which allows you to use all self-defence forces," Medvedev said on Telegram.
"This is why these referendums are so feared in Kyiv and the West. This is why they need to be carried out."
Ukraine warned on Tuesday that the Russian threat would be "liquidated" and denounced the planned referendums as "blackmail" motivated by "fear of defeat".
“Ukraine has every right to liberate its territories and will keep liberating them whatever Russia has to say," Foreign Minister Dmytro Kuleba wrote on Twitter.
The West has stated that such referendums would be illegal and would not be recognised.
5. UN General Assembly to focus on Ukraine war
The war in Ukraine is likely to dominate proceedings at the United Nations General Assembly in New York.
Zelenskyy has said that he would use his video address on Wednesday to call on countries to accelerate weapons and aid deliveries.
"We are doing everything to ensure Ukraine's needs are met at all levels - defence, financial, economic, diplomatic," the Ukrainian President said on Monday.
Kyiv has also called for a Nuremberg-style trial to be established to investigate atrocities committed by Russian troops.
So far, many countries have supported existing bodies, such as the International Criminal Court (ICC), for prosecuting such cases, but the Czech EU presidency has backed Kyiv's demands for a special international tribunal.
“In the 21st century, such attacks against the civilian population are unthinkable and abhorrent,” said Jan Lipavský, the Czech foreign minister. “We must not overlook it. We stand for the punishment of all war criminals.”
The UN General Assembly will also be the first foreign trip for UK Prime Minister Liz Truss, who has pledged to maintain UK military support for Ukraine.
In a statement, Truss said that her country expects to match or exceed the £2.3 billion (€2.6 billion) in military aid pledged this year by 2023.
"My message to the people of Ukraine is this: the UK will continue to be right behind you every step of the way. Your security is our security," Truss stated.
6. Russian lawmakers toughen punishment for soldiers
Russia’s lower house of parliament has approved new legislation that toughens punishment for soldiers who breach their duties.
Under the bill, military personnel could face severe penalties for failing to follow orders, deserting or surrendering to the enemy.
Those who voluntarily surrender to the enemy will also face a prison term of up to 10 years, and those convicted of looting could be handed a 15-year term.
The move by Russia's State Duma is an apparent effort to boost discipline in the ranks amid the war in Ukraine.
The bill will likely receive the upper house’s approval and must then be signed by President Vladimir Putin to become law.
Some nationalist politicians have called for a mobilisation to beef up the Russian military ranks, but the Kremlin so far has ruled it out.