Update at 3:21 p.m. ET
Pro-Russia rebels in Ukraine are no longer demanding full independence, telling negotiators in Belarus that they will respect Ukraine's sovereignty in exchange for autonomy.
The Associated Press adds:
"It's a shift that reflects Moscow's desire to strike a deal at a new round of peace talks — possibly avoiding tougher Western sanctions. The talks follow last week's meeting between the presidents of Russia and Ukraine. Similar talks earlier this summer produced no visible results."
Today's talks in Minsk, the capital of Belarus, lasted for several hours before being adjourned until Friday.
Earlier Monday, Russian Foreign Minister Sergei Lavrov said the meeting's goals should be a cease-fire, but he demanded that Ukrainian troops leave positions from which they can "harm the civilian population."
Karoun Demirjian, who is reporting for NPR from Moscow, tells our Newscast unit:
"[A] rebel leader in Donetsk told Russian news service Interfax that their main goal is to win recognition of their independence from Kiev.
"During a television interview, Russian President Vladimir Putin said statehood in eastern Ukraine should be one of the topics up for discussion; the Kremlin stressed, though, that Russia isn't directly supporting calls for independence.
"Meanwhile, Ukraine's military spokesman says that Russian formations were directly firing on troops at the Luhansk airport overnight. Russian-backed separatists say they seized the airport today."
Monday's meeting in Minsk comes a day after a Ukrainian border guard vessel was attacked near the eastern Ukrainian port city of Mariupol.
NPR's Soraya Sarhaddi Nelson, who is reporting from Mariupol for Newscast, says Ukrainian officials blamed Russian-backed separatists for the attack on the vessel patrolling in the Sea of Azov. She adds: "The separatist fighters last week launched an offensive along the coastline and now control several towns and villages here."
The crisis in Ukraine has resulted in the worst ties between Moscow and the West since the end of the Cold War.
Indeed, Sen. Robert Menendez, D-N.J., chairman of the Senate Foreign Relations Committee, told CNN on Sunday that the U.S. should "provide the Ukrainians with the type of defensive weapons that will impose a cost upon Putin for further aggression."
Sen. John McCain, R-Ariz., echoed those calls in an interview with CBS' Face the Nation.
"Give them the weapons they need," he said. "Give them the wherewithal they need. Give them the ability to fight."
In a news conference last week, President Obama blamed Russia for the violence in Ukraine. The administration's actions against Russia have so far mainly been limited to economic sanctions on Russia's banking, energy and defense sectors.
"Capital is fleeing, investors are increasingly staying out, his economy is in decline," Obama said last week. "This ongoing Russian incursion into Ukraine will only bring more costs and consequences for Russia."