The cease-fire in eastern Ukraine between Kiev's forces and the rebels is largely being observed but is still on "thin ice," a monitor from the Organization for Security and Cooperation (OSCE) in Europe said Thursday, one month after both sides agreed to the truce.

"The cease-fire holds broadly along the long contact line" in the eastern Donetsk and Lugansk regions, with crossfire continuing in some places but at a lower level, said Alexander Hug, deputy chief of the special monitoring mission the OSCE has dispatched to Ukraine.

The most critical locations were the village of Shyrokyne east of southeastern port of Mariupol and the areas surrounding the Donetsk airport, Hug said.

"In general it is positive that most of this fighting is being conducted with small arms and smaller caliber weapons and it's an indication that heavy weapons have actually been withdrawn and are not being used as often," he said in Kiev.

The OSCE has been trying to monitor the pullback of large artillery but the mission was still being hindered by both sides, Hug said, and did not have full inventories of weapons nor full access to sites where they may be stored.

As a consequence, Hug said the "relative stability is at the moment on thin ice" and that returning big guns back to the frontline would not take long.

Ukraine's security spokesman Andriy Lysenko said no soldiers had been injured or killed over the past day - the first time in five days.