President Vladimir Putin has ordered Russian troops to press their offensive deeper into the Donbas region of eastern Ukraine after Moscow's forces seized the strategic city of Lysychansk.

Russian Defence Minister Sergei Shoigu told Mr Putin at a meeting that Moscow's forces were now in full control of the Lugansk region.

In a sign there would be no let-up in the fighting and that Russia now had its eyes on the entire Donetsk region, Mr Putin told Mr Shoigu that troops stationed there must continue their operations.

"Military units, including the East group and the West group, must carry out their tasks according to previously approved plans," Mr Putin said.

"I hope that everything will continue in their direction as has happened in Lugansk so far."

The Ukrainian army said yesterday it was retreating from Lysychansk to preserve the lives of its troops who were outnumbered and outgunned by Russian forces.

With the war now well into its fifth month, Ukraine told a reconstruction conference in Switzerland today that it would already cost $750 billion to rebuild the country.

Leaders from dozens of countries and international organisations are attending the two day meeting in the Swiss city of Lugano, where they aim to hash out a roadmap for Ukraine's reconstruction - expected to cost hundreds of billions of euro.

"The key source of recovery should be the confiscated assets of Russia and Russian oligarchs," Ukrainian Prime Minister Denys Shmyhal told the conference.

Ukraine will also face demands for broad reforms, especially in cracking down on corruption after Brussels recently granted Kyiv candidate status in its push to join the 27-member bloc.

Ireland is also being represented at the conference with Minister for State at the Department of Finance Sean Fleming attending the meeting in Lugano.

He said the Ukraine Recovery Conference offered an opportunity for the international community to exchange ideas on reconstruction and to assist in co-ordination of the country's recovery.

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A woman stands in a crater caused by missile strikes which struck the yard of a school in Kharkiv

In a video address, Ukrainian President Volodymyr Zelensky described rebuilding Ukraine as the "common task of the whole democratic world" and the "biggest contribution to the support of global peace."

'Most modern weapons'

The loss of Lysychansk over the weekend prompted President Zelensky to step up calls for an increased supply of weapons from the West so Kyiv can keep up the resistance and regain lost territories.

After giving up on its initial war aim of capturing Kyiv following tough Ukrainian resistance, Russia has focused its efforts on securing control of the Donetsk and Lugansk areas which make up the Donbas region.

Moscow's capture of Lysychansk - one week after the Ukrainian army also retreated from the neighbouring city of Severodonetsk - frees up Russian forces to advance on Kramatorsk and Sloviansk in Donetsk.

Lugansk region governor Sergiy Gayday said on Telegram that there was still fighting in the town of Bilogorivka outside Lysychansk.

Smoke billows over the oil refinery outside the town of Lysychansk

"We keep defending a small part of the Lugansk region so that our army could build protective redoubts," he added.

In his address late yesterday, Mr Zelensky vowed Kyiv would fight on and ensure the military had "the most modern weapons".

"Ukraine will reach the level when the fire superiority of the occupiers will be levelled," he said.

In a symbolic boost, the Ukrainian flag was raised on Snake Island, a rocky outcrop in the Black Sea, after Russia withdrew from the strategically important Ukrainian territory last week.

In Sloviansk, about 75 kilometres west of Lysychansk, there were few people on the streets today, the day after Russian strikes that left at least six dead, among them a nine-year-old girl, and 19 injured.

In the large downtown market largely ravaged by a fire caused by a Russian strike, a few vendors offered basic goods while others cleared charred debris.

Vendors and residents who spoke to AFP, some still in shock, expressed concern for the days and weeks to come, as sounds of shelling were heard again.

The city of Siversk, 30 kilometres west of Lysychansk, also saw overnight shelling, residents and an official said.

Rescuers removed the body of a person from a destroyed building near Odesa

But President Zelensky's address yesterday evening was defiant, predicting Ukrainian troops would "win back" territory in the Donbas just as they had in other regions earlier in the war.

In the Swiss city of Lugano today where leaders from dozens of countries and international organisations met to hash out a roadmap for Ukraine's reconstruction, European Commission President Ursula von der Leyen said "Ukraine can emerge from this on a path towards a stronger and more modern country".

Lugano is not a pledging conference but instead is attempting to lay out the principles and priorities for a rebuilding process aimed to begin even as the war rages.

But for residents in Bucha - a Ukrainian town synonymous with war crimes blamed on Moscow's forces after their retreat in April - fear remains even as talk begins of reconstruction.

"We're going to bed without knowing if we'll wake up tomorrow," said 65-year-old Vera Semeniouk.

"Everyone has come back, is starting to repair houses, many are putting in new windows. It would be terrible if it started again, and we had to leave everything again."

On her first visit to Ukraine today, Swedish Prime Minister Magdalena Andersson visited Bucha and she also met with President Zelensky in Kyiv.

Magdalena Andersson and Volodymyr Zelensky at a joint press conference in Kyiv today

New Ukrainian defensive line

Rob Lee, of the US-based Foreign Policy Research Institute, said the new Ukrainian defensive line should be easier for Ukraine to defend than the pocket in Luhansk province it has given up.

"It's something that Putin can show as a sign of success," he said. "But overall, this doesn't mean Ukraine will have to concede or give in any time soon."

Dmitry Medvedev, deputy head of President Putin's security council, posted on social media that Ukraine was being egged on to keep fighting by Western leaders who "lose their minds at the sight of someone else's blood", and Ukraine's own rulers who were driven by "cocaine ecstasy".

Ukraine's hopes for a counter-attack rest in part on receiving additional weapons from the West, including rockets that can neutralise Russia's huge firepower advantage by striking deep behind the front line.

Last week, Ukraine scored its own major victory, driving Russian forces off Snake Island, a desolate but strategic outcrop in the Black Sea that Moscow had captured on the war's first day but could no longer defend from Ukrainian strikes.

Ukraine's military said today it had now hoisted its flag there.