(CNN) - John McCain and Barack Obama both spoke to Georgia's president Saturday and continued to call for an end to Russia's bombing of the former Soviet republic.
Both candidates pressed for recognition of Georgia's sovereignty pushed for diplomacy in the conflict.
"For many years, I have warned against Russian actions that undermine the sovereignty of its neighbors," said McCain, the presumptive Republican nominee, on Saturday. "Unfortunately, we have seen in recent days Russia demonstrate that these concerns were well-founded."
Obama also condemned "the violation of Georgia's sovereignty" and called for "an immediate ceasefire."
"Russia must stop its bombing campaign, cease flights of Russian aircraft in Georgian airspace, and withdraw its ground forces from Georgia," Obama said.
McCain said he has spoken to Georgian President Saakashvili twice since the conflict began. "It is clear the situation is dire ... I again call on the government of Russia to immediately and unconditionally withdraw its forces from the territory of Georgia."
He called the conflict a "threat to Euro-Atlantic security," and supported attempts by Western powers - including the United States, the European Union, and NATO - to broker a ceasefire.
Obama is receiving breifings om the situation while on vacation in Hawaii. He also spoke with Saakashvili, and in a statement afterwards direct talks between Russia and Georgia are necessary.
"Diplomats at the highest levels from the United States, the European Union, and the United Nations must become directly involved in mediating this military conflict and beginning a process to resolve the political disputes over the territories of South Ossetia and Abkhazia," he said. "A genuinely neutral mediator - not the Russian government - must begin a process of negotiations immediately."