This post was updated at 5:10 p.m. ET.
U.S. Secretary of State John Kerry said all sides agree that the crisis on the Crimean Peninsula must be resolved through dialogue, but he acknowledged there has yet to be one-on-one discussions between Russian Foreign Minister Sergey Lavrov and his Ukrainian counterpart.
At a news conference following meetings in Paris that included Ukrainian Foreign Minister Andriy Deshchytsia and the foreign ministers of France, German and Britain, Kerry said all sides would "be served better if this can be resolved through dialogue."
Though nothing concrete had been decided, he said, they "agreed [to] continue intense discussions in the coming days with the Russians, with the Ukrainians in order to see how we can help normalize the situation, stabilize it and overcome the crisis."
Kerry added that he thought the discussions in Paris were constructive.
"I personally feel as if I have something concrete to take back and talk to President Obama about so that I can get his input and thinking, advice on what he's prepared to do," he said. "And I believe that Foreign Minister Lavrov is in exactly the same position with respect to President Putin."
Given the tensions in the region, Kerry called the situation "hard, tough stuff." On the other hand, he said, "I'd rather be where we are today than we were yesterday."
Kerry acknowledged there had been no face-to-face meeting between Lavrov and Deshchytsia, but said, "I had no expectation, zero expectation, that today that kind of a meeting would take place."
Kerry also sounded the requisite tough line on Russia's actions to increase troop levels in Crimea, ostensibly at the invitation of the pro-Russian government there. "We cannot and will not allow the integrity of the sovereignty of the country of Ukraine to be violated and for those violations to go unanswered," he said.
Kerry also referenced comments made by Defense Secretary Chuck Hagel in testimony before the Senate Armed Services Committee that the U.S. was stepping up joint aviation training with Polish forces and that the Pentagon was increasing American participation in NATO's air policing mission in its Baltic members, Estonia, Latvia and Lithuania, all former Soviet states.
Reuters, quoting an unnamed U.S. official, reported that six additional F-15s and a KC-135 refueling aircraft were being deployed to augment that mission.
Lavrov, on leaving the Paris meetings, said more talks would take place "in days to come."
"We are all concerned at what it is happening there," he told reporters on leaving the French Foreign Ministry.
On Tuesday, as we reported, Kerry and President Obama said Russia's explanation for its actions in Ukraine doesn't line up with reality.
Russian President Vladimir Putin "can throw a lot of words out there," Obama said, "but the facts on the ground" indicate that Russia is not acting in accordance with international principles about how to treat sovereign neighbors.
Kerry, who visited Kiev on Tuesday, said the U.S. condemns Russia's "act of aggression."
Putin said the soldiers who have surrounded Ukrainian military bases in Crimea and taken over key government installations are not Russian troops, but his statement flies in the face of what eyewitnesses and reporters such as NPR's Peter Kenyon, who is in Crimea, are seeing.
The U.S. and other Western nations say they hope Russia will take what's being called a diplomatic "off-ramp" — perhaps accepting the presence of international monitors in Crimea who would protect the interests of the region's ethnic Russian majority.
Earlier Wednesday in Madrid, where he has been meeting with Spanish officials, Lavrov said it's not up to Russia to decide whether international monitors should go to Crimea. That decision must be made by authorities in Ukraine and Crimea, which enjoys autonomy, he said.
From Madrid, correspondent Lauren Frayer tells our Newscast Desk that Lavrov also repeated Putin's claim that the troops in Crimea are "local self-defense forces" that don't answer to Moscow.
Also Wednesday, there was word from Brussels that European Union officials have agreed to provide Ukraine with a $15 billion package of loans and grants to shore up its economy, which has been crippled by the crisis.
We've previously summed up what set off months of protest in Kiev and ultimately led to Ukrainian President Viktor Yanukovych's dismissal by his nation's parliament last month:
"The protests were sparked in part by the president's rejection of a pending trade treaty with the European Union and his embrace of more aid from Russia. Protesters were also drawn into the streets to demonstrate against government corruption."
It was after Yanukovych left Kiev and headed for the Russian border that troops moved to take control of strategic locations in Crimea. That peninsula is important to Russia not only because of the large ethnic Russian population, but also because it's home to Russia's strategically significant warm-water naval base on the Black Sea.