Ukrainian President Petro Poroshenko says he has agreed to an international humanitarian mission for eastern Ukraine led by the Red Cross that includes cooperation from the European Union, Germany, and Russia.
Poroshenko said the mission has the blessings of Russia and the United States.
But he said any humanitarian mission must be "an international one without any military escort" by Russian forces.
Poroshenko also said European Commission President Jose Manuel Barroso pledged more than $3 million of European humanitarian aid for eastern Ukraine on August 11.
In Washington, the White House said President Barack Obama and Poroshenko agreed by telephone that "any Russian intervention in Ukraine without the formal, express consent and authorization of the Ukraine government would be unacceptable and a violation of international law."
The Kremlin says Russian President Vladimir Putin told Barroso on the same day that Moscow is sending a "humanitarian" convoy into Ukraine with Red Cross supervision. It said there would not be any Russian military escort.
Barroso warned Putin against any unilateral military action in Ukraine under any pretext, including humanitarian.
NATO Secretary-General Anders Fogh Rasmussen said earlier on August 11 that he saw a "high probability" of Russia trying to intervene militarily in Ukraine "under the guise of a humanitarian operation."
Rasmussen said Russia is "developing the narrative and the pretext" for illegal military operations in Ukraine.
He said NATO sees no sign that Moscow is pulling back some 20,000 troops that it has deployed close to Russia's border with Ukraine, and that the military buildup "could be used to conduct such illegal military operations in Ukraine."
Ukraine's Foreign Ministry told RFE/RL's Ukrainian Service on August 11 that it had not agreed to Russian convoys working on their own without international cooperation or monitors.
Sitara Jabeen, a spokeswoman for the International Red Cross, said on August 11 that he organization would only be involved in aid deliveries into eastern Ukraine if they were carried out "according to our own principles, according to our own modalities."
Jabeen said the Red Cross has made it very clear to Russia's Foreign Ministry that it would only distribute aid if all parties -- Moscow, the government in Kyiv, and pro-Russian separatists -- accept the Red Cross as "a neutral and impartial organization."
Later on August 11, Laurent Corbaz, the head of Red Cross operations for Europe and Central Asia, said in a statement that all sides must guarantee the security of Red Cross workers because the organization will not take part in any aid delivery mission that involves military escorts.
Corbaz also said it needs to receive "without undue delay" from Russia "all necessary details concerning the aid, including the volume and type of items, and requirements for transport and storage."
Lavrov criticized the United States, Britain, and France on the issue on August 11 over the issue of humanitarian deliveries -- claiming that Western powers oppose any humanitarian aid going into eastern Ukraine.
However, those Western powers only oppose the idea of Moscow using a humanitarian mission as an excuse to deploy Russian military forces into eastern Ukraine.
Ukraine's Interior Ministry says Russia has tried to send military convoys into Ukraine -- claiming the convoys contained humanitarian aid, but bypassing Ukrainian customs by crossing the border in areas under the control of pro-Russian separatists.
Kyiv and Western powers say Russia has used those areas in the past to deliver weaponry to the separatist fighters.
Meanwhile, Ukrainian military forces on August 11 continued to shell the pro-Russian separatist bastion of Donetsk.
Ukrainian military spokesman Andriy Lysenko said on August 11 that Ukraine's army had cut Donetsk off from Luhansk, the other main separatist-held city in eastern Ukraine.
Lysenko also said Russian aircraft had violated Ukrainian airspace at least five times since August 10 and that Moscow's forces continue to fire artillery barrages from Russian territory at Ukrainian troops who are battling the pro-Russian separatists in the east.
Lysenko also said a total of 568 Ukrainian troops have been killed during the past four months of fighting and that 2,120 soldiers had been wounded.
With reporting by RFE/RL's Ukrainian service, Reuters, AP, AFP, ITAR-TASS, and Interfax