(Adds comments from former Russian president, Swiss right-wing party, details on draft communique)

BUERGENSTOCK, Switzerland, June 16 (Reuters) - Western powers and other nations sought a consensus on the second day of a summit in Switzerland on Sunday on condemning Russia's invasion of Ukraine and underscoring the war's human cost.

A draft of the final summit declaration seen by Reuters refers to Russia's invasion as a "war" - a label Moscow rejects - and calls for Ukraine's control over the Zaporizhzhia nuclear plant and its Azov Sea ports to be restored.

The draft, dated June 13, called for Ukraine's territorial integrity to be respected.

But - in line with the conference's more modest stated aims - it omitted knottier issues of what a post-war settlement for Ukraine might look like, whether Ukraine could join the NATO alliance or how troop withdrawals from both sides might be managed.

Moscow casts what it calls its special military operation in Ukraine as part of a broader struggle with the West, which it says wants to bring Russia to its knees, while Kyiv and the West say Russia is waging an illegal war of conquest.

World leaders including U.S. Vice President Kamala Harris, German Chancellor Olaf Scholz and French President Emmanuel Macron gathered at the mountaintop resort of Buergenstock in a bid to bolster international support for ending the war.

Many Western leaders voiced forceful condemnation of the invasion and rejected Russian President Vladimir Putin's demands for parts of Ukraine as a condition for peace.

"One thing is clear in this conflict: there is an aggressor, which is Putin, and there is a victim, which is the Ukrainian people," Spanish Prime Minister Pedro Sanchez said.

More than 90 countries took part, but China's decision to stay away dimmed hopes that the summit would show Russia was globally isolated, while recent military reverses have put Kyiv on the back foot.

Some leaders departed early, and talks on Sunday will turn towards pursuing a joint position on the need for nuclear and food security, and the return of prisoners of war and children removed from Ukraine during the conflict.

White House National Security Adviser Jake Sullivan told reporters that Qatar had helped to mediate the return from Russia of 30 or more Ukrainian children to their families.

"It's going to take international pressure. It's going to take a spotlight from the international community – and not just from the voices from the United States or Europe – but from unusual voices, as well, to say what Russia has done here is morally reprehensible and must be reversed," he said.

Kyiv says about 20,000 children have been taken to Russia or Russian-occupied territory without the consent of family or guardians since the war began. Moscow rejects this, saying it has protected vulnerable children from the war zone.

The draft communique calls for all illegally deported children to be returned.

FOLLOW-UP

Ukrainian President Volodymyr Zelenskiy hailed the summit at the resort overlooking Lake Lucerne as a show of international support for Kyiv, even as some European allies said a broader outreach was needed for a lasting peace plan.

One central ambition of the Swiss and Ukrainian organisers is to announce on Sunday the host country for a follow-up conference meant to build on the Swiss momentum, although the draft communique made no mention of this.

Saudi Arabia is one of the favourites, and Foreign Minister Prince Faisal bin Farhan Al Saud said the kingdom was ready to assist the peace process, but warned that a viable settlement would hinge on "difficult compromise."

Striking a balance in the summit's final declaration between forthright condemnation of Russia's invasion of Ukraine and wording that commands the broadest possible support has been part of the diplomatic tug-of-war at the event, sources say.

Russia has dismissed the summit as a waste of time.

"None of the participants in the 'peace forum' knows what he is doing there and what his role is," said Dmitry Medvedev, Russia's former president and now deputy chairman of the country's Security Council.

Switzerland also faced some internal criticism. Nils Fiechter, a member of the right-wing Swiss Peoples' Party (SVP), the biggest group in the Swiss lower house of parliament, appeared on broadcaster Russia Today to call the summit a "farce".

He warned that the summit undermined Swiss neutrality and said Russia had to have a seat at the table.

It remains to be seen how many countries will back a final joint declaration, and Austrian Chancellor Karl Nehammer on Saturday sought to temper hopes somewhat.

"Just to manage expectations, please: The crucial take-away is that we've all come here, that we're talking, that many different nations and continents are talking to each other ... This is the essence of this conference," he said.

"Peace and peace processes take time, working millimetre by millimetre."

(Reporting by Steve Holland, Thomas Escritt, Sabine Siebold, Dave Graham; Writing by Dave Graham and Matthias Williams; Editing by Mark Potter and Hugh Lawson)