Slovyansk, Ukraine (CNN) -- Ten Russian soldiers were detained in the Donetsk region of eastern Ukraine, that country's Security Service said Tuesday, as tensions simmered over the conflict between Ukrainian forces and pro-Russian rebels.
The Russian soldiers were captured with documents and weapons on them, the Security Service said.
Moscow has repeatedly denied claims by Kiev that it has sent troops and weapons over the border into Ukraine, where the Ukrainian military is fighting pro-Russian rebels.
Russia's state-run RIA Novosti news agency cited a source in the Russian Defense Ministry as saying the soldiers had been patrolling the border and "most likely crossed by accident" at an unmarked point.
The development came as Ukrainian President Petro Poroshenko and his Russian counterpart, Vladimir Putin, met for the first time since June.
The two Presidents agreed that they need to "renew our dialogue," Putin said, according to a CNN translation.
Putin said the meeting was "positive."
The two leaders are in Minsk, the capital of Belarus, for talks related to the Eurasian Customs Union, a trade bloc made up of Russia, Belarus and Kazakhstan -- with the crisis in Ukraine expected to dominate.
As the talks started, Poroshenko said "the fate of the world and Europe" could be decided in Minsk. "We must jointly find the only right decision. Peace on the continent depends on it," he said, according to his office.
Senior European Union officials, headed by EU foreign policy chief Catherine Ashton, are also in Minsk for the summit.
"The EU is attending to see if discussions can help create momentum for a new political solution to the crisis in Ukraine," said Ashton's spokeswoman, Maja Kocijancic.
Putin told reporters that Russia couldn't be involved in ceasefire talks because those discussions should be between Kiev and separatists in eastern Ukraine. Moscow is willing to assist, he added.
Putin: Military escalation won't solve crisis
Putin was cited by Russian state media as telling fellow leaders that the crisis in Ukraine "cannot be solved through further escalation of the military scenario."
He said Russia was "ready to exchange opinions" on the conflict and urged dialogue to find a peaceful resolution, state news agency ITAR-Tass reported.
Earlier, Poroshenko spoke with Ashton about the situation in his country's east and the detention of the 10 Russian soldiers, his office said.
He urged the world to support Ukraine and its efforts to secure its border with Russia "to prevent cross-border infiltration of weapons, military equipment and mercenaries." This, he said, would swiftly resolve the situation.
The conflict was first sparked last year by a political crisis over whether Ukraine would seek closer ties with Europe or with Russia. The ouster of pro-Moscow President Viktor Yanukovych in February was followed by Russia's annexation of Ukraine's Crimea region in March and a declaration of independence by separatist leaders in the Donetsk and Luhansk regions.
Poroshenko in June signed a landmark EU trade pact, despite opposition from Russia.
On Tuesday, after meeting with Ashton, the President said Ukraine would ratify the Association Agreement with the European Union in September and immediately send the ratification documents to Brussels.
The move "is in no way aimed against anyone," Poroshenko said, according to a statement from his office. "Instead, the agreement will positively affect relations with all our neighbors, especially in the economic sphere. We would like our international partners to accept our decision."
He added that parliamentary elections scheduled for October 26 should not affect the EU agreement. Poroshenko's trip to Belarus comes a day after he dissolved Ukraine's parliament.
However, Putin warned that it would cost Ukraine billions of euros to try to meet EU trade standards and that Russia, Belarus and Kazakhstan would also lose out. Ukrainian imports would no longer be given preferential treatment, he added.
It's not yet been confirmed whether Putin and Poroshenko, who last met briefly during D-Day commemorations in France, will hold bilateral talks while in Minsk.
'I just want to survive'
Meanwhile, fighting continues for control of Luhansk and Donetsk, both strongholds for the rebel fighters.
Ukraine's National Defense and Security Council said Tuesday that militants and the Russian military have become more active in the east and south of Donetsk, as well as along the border, with 29 clashes in the past day.
Rebel fighters continue to cross the border, backed up by the Russian military firing over the border, NDSC spokesman Col. Andriy Lysenko told reporters at a briefing.
Four Ukrainian border guards died and three were injured when two Russian Mi-24 helicopters fired on them, he said.
Russia denies direct or indirect involvement in the fighting and says Ukraine's assault against the rebels is precipitating a humanitarian crisis.
The besieged city of Luhansk has been without water and power for over three weeks, city officials said Sunday. Shelling has caused major damage there and in surrounding villages over past weeks.
Members of the Mahounin family told CNN how they fled their town two days earlier. Intense shelling meant they'd had to spend 24 hours a day in an underground bomb shelter with more than 100 others.
"I don't care what they're fighting for, I just want to survive -- I want my son to survive," said Lilia Mahounin.
Lavrov told reporters that Russia hopes to send a second humanitarian aid convoy to Ukraine this week to help civilians caught up in the conflict.
Last Friday, a convoy of 227 Russian trucks crossed that country's border into eastern Ukraine without Kiev's authorization, a move condemned by international powers as a violation of Ukraine's sovereignty. Officials in Kiev referred to it as an invasion.
The trucks left a day later, having successfully delivered supplies to Luhansk, Russian authorities said. Ukrainian authorities said they suspected the delivery had been used to bolster rebel forces.
U.N. officials estimate that more than 2,000 people have died and nearly 5,000 have been wounded in eastern Ukraine since mid-April.
German Chancellor Angela Merkel, on a weekend visit to Kiev, promised Ukraine loans worth 500 million euros to help rebuild shattered infrastructure and homes.
CNN's Diana Magnay reported from Slovyansk, journalist Victoria Butenko reported from Kiev, and CNN's Laura Smith-Spark wrote and reported in London. CNN's Alla Eshchenko and Matthew Chance in Moscow contributed to this report.