Government forces lost more ground to Russian-backed separatists in heavy fighting in eastern Ukraine on Sunday, a day after European leaders threatened to impose more sanctions on Moscow if it doesn't end its support for the rebels.

Ukrainian President Petro Poroshenko said he hoped a new round of talks with rebels and Russian officials in Minsk on Monday could yield progress toward a cease-fire. It wasn't clear whether Kiev was ready to accept a deal that would leave the separatists in control of their strongholds in the cities of Luhansk and Donetsk.

Previously, Mr. Poroshenko had vowed to defeat them unless they surrendered. But after dramatic reversals on the battlefield in recent days--following what Kiev and the North Atlantic Treaty Organization say was an incursion of more than 1,000 Russian troops to fight alongside the separatists--his negotiating position seems weakened. European leaders were cool to his appeals for military aid and held off immediately imposing more sanctions to give Russia a chance to change course.

The Kremlin on Sunday stepped up its calls for Kiev to lay down its arms and begin talks, effectively recognizing the Moscow-backed rebels" hold over a major industrial region. Moscow also hinted at support for the rebels" demands for independence.

President Vladimir Putin, in an interview on state television Sunday, said Kiev should begin "substantive, meaningful negotiations, and not on technical issues, but on the political organization of society and statehood in the southeast of Ukraine."

A Kremlin spokesman later told reporters that the reference to "statehood" wasn't meant as an endorsement of the separatists" demands for independence from Ukraine. But the spokesman said Ukraine would have to discuss autonomy with a region he referred to as "Novorossiya." That tsarist-era word, referring to a swath of territory that includes much of present-day southern and eastern Ukraine, has become a rallying cry for Russian nationalists. It had faded from official Kremlin statements since the spring but reappeared this week.

The latest events on the ground were a dramatic reversal for Kiev, whose forces had been close to retaking the rebel strongholds in Donetsk and Luhansk in early August, officials said. The introduction of several units of Russian troops over the past week or so has dramatically turned the tide.

Security officials in Kiev say the combination of Russian troops, tanks and antiaircraft systems--which helped neutralized Kiev's advantage in air power--allowed the separatists to reopen key supply lines to Luhansk and Donetsk and open a new front for the strategic port city of Mariupol. Moscow denies deploying troops, though rebels say Russian military personnel are fighting on their side, though while on vacation.

On Sunday, Ukraine exchanged 10 Russian paratroopers captured on its territory early last week for 63 Ukrainian troops who had crossed into Russia after becoming surrounded. Moscow has said the paratroops crossed into Ukraine by accident.

Ukraine's setbacks have prompted alarm among Western officials, but little signs of outright military aid.

Mr. Poroshenko returned Sunday from a European Union summit in Brussels after the EU agreed to draw up options within a week for possible new sanctions against Russia. He left, though, without any promise of military support from the bloc's 28 governments.

In Washington, the White House welcomed the EU's moves and said it remained committed to a diplomatic solution. But some legislators said the sanctions weren't enough.

"If you're looking at it from Vladimir Putin's viewpoint, he's done pretty well with minimum of penalty and as long as the Europeans are dependent on his energy supply, they're not going to do much," Sen. John McCain (R., Ariz.) said on CBS's Face the Nation.

He added the U.S. should provide Ukraine's military with weapons and battlefield intelligence. "For God's sake, can't we help these people defend themselves?" he said.

While European leaders said there was a clear determination to press ahead with sanctions if Russia didn't scale back its intervention, European Council President Herman Van Rompuy said leaders hadn't defined clear criteria for triggering fresh measures at Saturday's meeting. But governments were ready to quickly move ahead given the deterioration of the situation in eastern Ukraine, he said at a postsummit news conference.

On Saturday, after a meeting with Mr. Poroshenko, European Commission President José Manuel Barroso warned the situation was approaching "a point of no return." He said the bloc hoped to see a cease-fire but made clear that any agreement would necessitate a withdrawal of Russian troops and quick measures to genuinely stem the flow of weapons and fighters over the border.

A senior EU aide who participated in Saturday's summit said that such conditions would likely be the prerequisite for any decision to delay sanctions.

"A strict conditionality for "what if" wasn't discussed, [but] the criteria would be the same as last time: cease-fire with secured border and international monitoring would represent a positive step," the aide said.

The aide said the bloc won't support steps that allow Russia to turn eastern Ukraine into a permanent conflict zone that Moscow can use to openly exert its influence. A cease-fire must lead to "a process of disarming militias and national dialogue, decentralization with Donbas as part of Ukraine," he said.

Still, some member states remain wary about pursuing tougher measures, partly because of concerns about economic retaliation. Some governments also believe that economic tensions will make a political solution less likely.

Any further sanctions will need unanimous support among the EU. A handful of countries--including Hungary, Slovakia, Cyprus and Austria--have aired concerns about ramping up sanctions. Austrian Chancellor Werner Faymann, on his way into Saturday's meeting, was blunt about those concerns, although he didn't rule out increasing economic pressure if Moscow continued to block a political solution.

"The effect of sanctions as they have been applied so far hasn't always produced what some expected," he said. "We should be speaking less about sanctions," he said.

William Mauldin in Washington contributed to this article.

Write to Alan Cullison at alan.cullison@wsj.com

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