Ukrainian President Petro Poroshenko announced Monday that an international humanitarian mission would be sent to the war-torn east of his country, in a fragile move toward peace on a day in which fighting continued unabated.

The announcement came shortly after the Kremlin said it was sending a “humanitarian convoy” of its own to Ukraine with the support of the International Committee of the Red Cross. The Kremlin did not provide details about the timing or the form in which the aid would be delivered.

With Western officials warning that any unilateral moves by Russia would be treated as an invasion and NATO’s top official saying Monday that there was a “high probability” that Russia would invade Ukraine, the Kremlin statement appeared to take Ukrainian leaders by surprise.

Minutes after the Russian announcement, Poroshenko spoke to President Obama by telephone. After that conversation, Poroshenko’s office said that the international humanitarian mission would take place and that Obama had assured him of U.S. willingness to join in the efforts in the eastern region of Luhansk.

Poroshenko agreed to an “international humanitarian mission for Luhansk under the aegis of the International Committee of the Red Cross with participation of the E.U., Russia, Germany and other partners,” his office said. “Barack Obama confirmed the intention of the USA to take active part in the international humanitarian mission.”

Ukrainian government soldiers from battalion "Donbass" walk through a field as they search from house to house in the village of Mariinka near Donetsk, eastern Ukraine. (Evgeniy Maloletka/AP)

The White House said after the call that Obama “noted the urgency of such humanitarian efforts,” but it stopped short of announcing any U.S. aid commitments. It also said 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.”

A Foreign Ministry spokesman, Yevhen Perebyinis, said Ukraine had told Russia that it would accept humanitarian aid only if it was delivered via U.N. or Red Cross channels and through Ukrainian-controlled border checkpoints .

No details were given about when the aid would reach residents, and there were warning signs that the help might not be imminent.

“The practical details of this operation need to be clarified before this initiative can move forward,” Laurent Corbaz, the head of Red Cross operations in Europe and Central Asia, said in a statement.

The Red Cross said Monday that if Russian authorities “hand over” humanitarian aid, the organization was ready to distribute it with the “involvement, endorsement and support of all sides concerned.” But it said Russia still needed to specify what kind of aid would be provided.

The Red Cross said that because it does not accept armed escorts, “all parties” must guarantee the security of its staff and vehicles. That would include the pro-Russian rebels in the affected region, who have at times fought among themselves about how to treat international organizations on the ground. Heavily armed rebel escorts accompanied observers from the Organization for Security and Cooperation in Europe as they traveled the Donetsk region after the shooting down of Malaysia Airlines Flight 17 last month, and they at times complained about their access to the crash site.

The aid measures may help ease the growing crisis in the east, where about 250,000 residents who remain in the city of Luhansk have been without electricity or water for nine days, according to officials there.

But even if aid does reach those residents, Ukraine appeared to have no intention of stopping its military operations in the region. Heavy fighting continued Monday in Donetsk, about 75 miles away, as officials vowed to retake the rebel stronghold.

The Kremlin said Russian President Vladimir Putin had told E.U. Commission President José Manuel Barroso that “Russia, working together with International Red Cross officials, is sending a humanitarian convoy to Ukraine.”

Barroso’s office said that in his conversation with Putin, he had “warned against any unilateral military actions in Ukraine, under any pretext, including humanitarian.” A Barroso spokesman later said that Putin would send the aid through international organizations.

Separately on Monday, NATO Secretary General Anders Fogh Rasmussen said there was a “high probability” of a Russian military intervention in Ukraine.

“We see the Russians developing the narrative and the pretext for such an operation under the guise of a humanitarian operation, and we see a military buildup that could be used to conduct such illegal military operations in Ukraine,” Rasmussen told the news agency Reuters.

Intense fighting continued Monday as Ukrainian forces pressed in on Donetsk, which rebels have said is surrounded. Rockets late Sunday hit a high-security prison, killing one inmate and wounding three, the Associated Press quoted a city official as saying. The city’s Web site said Monday that 64 inmates escaped after the attack.

Military personnel repeated calls for civilians in Donetsk and Luhansk to leave if possible, warning that military action could continue for weeks. Since fighting began in April, 568 Ukrainian troops have been killed and 2,120 have been wounded, Ukrainian military spokesman Andriy Lysenko told reporters in Kiev on Monday.

Russia has massed 45,000 troops on the border with Ukraine, Lysenko said. He said the buildup included 160 tanks, 390 artillery systems, 1,350 armored vehicles, up to 150 Grad multiple-rocket launchers, 192 combat aircraft and more than 100 attack helicopters. NATO estimated last week that there were 20,000 troops on the border.

Russia on Monday launched a new round of military exercises involving about 3,000 personnel near the border with Estonia.

Julie Tate in Washington and Karoun Demirjian in Moscow contributed to this report.