Pro-Russian rebels are pressing to seize a key airport in eastern Ukraine despite fierce resistance by government forces.

Rebel tanks were reported firing at the main terminal of Donetsk airport, where government forces are holed up, and sniper shots rang around the area.

Ukraine's National Security and Defence Council said two Ukrainian servicemen had been killed and nine wounded since yesterday.

Fighting for the airport has intensified this week, threatening to derail a truce declared on September 5. A follow-up deal requesting both parties to pull back their artillery to create a buffer zone has not been implemented.

Residential areas in Donetsk have been caught in the crossfire. A Red Cross staffer died yesterday when a shell landed near the group's office in the city.

Rebels have made some gains in the area near the airport, seizing buildings on its fringes and using them to target the main terminal.

Security and defence spokesman Colonel Andriy Lysenko said Ukrainian forces at the airport have undergone rotation and firmly stood their ground.

The airport, just north of Donetsk, the largest city in the east, gives Ukrainian forces a convenient vantage point to target rebel positions. Its loss would be a major blow to Kiev and would also allow rebels to receive large cargo planes with supplies in addition to truck convoys from Russia.

The rebels said the shelling that killed the Red Cross worker came from the Ukrainian side, but Ukrainian foreign minister Pavlo Klimkin blamed the death on "terrorists".

A spokesman for UN secretary-general Ban Ki-moon issued a statement, saying the aid worker's death and the shelling of a school that killed three people earlier this week "underscore the fragility of the current ceasefire and the importance of ensuring a secure environment in south-eastern Ukraine that will allow humanitarian actors to carry out their work and deliver critical assistance to those most in need".