Dozens of countries meeting for a landmark international summit on peace in Ukraine agreed Sunday that Kyiv should enter dialogue with Moscow on ending the war, while strongly supporting Ukraine's independence and territorial integrity.More than two years after Russia launched its full-scale invasion, leaders and top officials from more than 90 countries spent the weekend at a Swiss mountainside resort for a two-day summit dedicated to bringing an end to the war."We believe that reaching peace requires the involvement of and dialogue between all parties," read a final communique, which was supported by the vast majority of the countries that attended the summit at the Burgenstock complex overlooking Lake Lucerne.The document reaffirmed a commitment to the "territorial integrity of all states, including Ukraine," while also urging a full exchange of prisoners of war and the return of deported children.But not all attendees backed the document, with India, Saudi Arabia and the United Arab Emirates among those not included in a list of supporting states displayed on screens at the summit.The day before, Ukrainian President Volodymyr Zelensky said he hoped to garner international support for a proposal to end the war that he could eventually present to Moscow.Sunday's part of the summit focused on food security, avoiding a nuclear disaster and returning deported children from Russia as countries outlined building blocks toward ending the war.The summit, snubbed by Russia and its ally China, comes at a moment when Ukraine's military faces increased pressure on the battlefield, with Russia last month launching a new ground offensive against the northeastern Kharkiv region.On Friday, Russian President Vladimir Putin demanded Kyiv's effective surrender as a basis for peace talks.Putin's call for Ukraine to withdraw from the south and east of the country was widely dismissed at the summit.But the Kremlin insisted Sunday that Ukraine should "reflect" on Putin's demands, citing the military situation on the ground."The current dynamic of the situation at the front shows us clearly that it's continuing to worsen for the Ukrainians," Kremlin spokesman Dmitry Peskov said."It's probable that a politician who puts the interests of his country above his own and those of his masters would reflect on such a proposal."