A spokesman for the regional administration said the separatists apparently wanted to use the clinic to provide treatment for injured fighters.
Ukraine's Border Guard Service, meanwhile, said eight crossings on the border with Russia in Donetsk and neighboring Luhansk region were temporarily closed on June 6 after heavy fighting.
Among those was the border crossing near the town of Marynivka, some 95 kilometers east of Donetsk, where the agency said 15 separatists were killed and five border guards wounded in overnight clashes.
Ukraine's government has said separatist fighters are crossing the border from Russia.
Russia's Foreign Ministry said it was "outraged" by the closure of the border crossings. (UNIAN, Interfax, and RFE/RL's Ukrainian Service)
Margrethe II of Denmark buffers Putin at @fhollande's cramped #DDay luncheon table pic.twitter.com/S2CCQiQ3mL by @MRWichmann v @crusoes
— Nikolaus von Twickel (@niktwick) June 6, 2014
!!! BREAKING NEWS !!!
Voice of America: Putin, meets Obama, Poroshenko on D-Day event sidelines http://t.co/Fcd2mVoEWg
— Kyiv Post (@KyivPost) June 6, 2014
Putin and Poroshenko met briefly on the sidelines of D-Day anniversary events in France today.
It was Putin's first meeting with Poroshenko since he was elected president of Ukraine on May 25.
Putin also held informal talks with U.S. President Barack Obama on the sidelines of the ceremonies.
The events to mark the 70th anniversary of the D-Day landings of Allied troops in Normandy came amid a deep rift between Russia and Western nations over Moscow's actions in Ukraine.
The events were preceded by intense diplomacy in the hope that the gathering of world leaders would lead to a thaw in tensions.
MT @ADeshchytsia. On 70th anniversary of #DDay70, let's not forget that 1/4 of all Ukrainians died in WW2. Highest ratio of any nation?
— Gulliver Cragg (@gullivercragg) June 6, 2014
Happy together. Merkel & Putin today for #DDay70 ceremony. http://t.co/N88htmy46T pic.twitter.com/7Mgs6ElSqe
— Jim Roberts (@nycjim) June 6, 2014
Gravity of the moment there, Putin aside from others, Poroshenko on the other end pic.twitter.com/fBYJJJx1kP via @pavelsheremet
— Ryskeldi Satke (@RyskeldiSatke) June 6, 2014
The unidentified official said today that the negotiations are to take place from June 7 to June 9.
The official also said Kyiv is considering paying off debts for last year's Russian supplies.
A spokeswoman for the EU’s energy commissioner told the ITAR-TASS news agency that the dates for the talks have not been confirmed yet.
The two sides differ on how much is owed by Ukrainian state energy company Naftohaz and the pricing for Russian gas.
Russia more than doubled the price Ukraine has to pay for gas -- to nearly $500 per 1,000 cubic meters -- after pro-Russian President Viktor Yanukovych was ousted in February.
Look at Johnny-no-mates on the right and the attention the nice old lady on the left is getting HT @BDStanley pic.twitter.com/rStTl42cD6
— john sweeney (@johnsweeneyroar) June 6, 2014