The US and Russia have agreed to exchange information about the situation on the Russia-Ukraine border, according to US Secretary of State John Kerry.

Russian Foreign Minister Sergei Lavrov said if the US got involved to help resolve the conflict it would be “a step in the right direction”.

After their meeting in Beijing in the lead-up to the Asia-Pacific Economic Cooperation (APEC) summit, both admitted however that they do not see eye to eye on events in Ukraine.

“We do have some disagreements about some of the facts on the ground with respect to Ukraine. We have agreed to exchange some information between us regarding that. And we have also agreed this is a dialogue that will continue,” Kerry said.

Lavrov said the US should discourage what he called “hot heads” among Ukraine’s leadership from resuming an all-out conflict with the rebels.

“The ceasefire has been signed between the rebels and the government. It’s for them to finalise the disengagement line which they are doing right now,” the Russian foreign minister said.

He laughed off Kyiv’s claims that there’d been a new Russian military incursion into eastern Ukraine this week.

Lavrov noted that the US government on Friday said that it was aware of the reports, but could not independently confirm them.

“Even (spokeswoman) Jen Psaki said that the State Department doesn’t have the information about this,” he said. “Well, if Psaki doesn’t have it, I don’t.”

More fighting was reported in Donetsk overnight, underlining the ceasefire’s fragility.

The Ukrainian army says one soldier was killed by a sniper at the airport, and 15 other soldiers were injured in various clashes, along with two civilians.

Municipal authorities in Donetsk also said two civilians had been wounded after a night marked by shots and explosions.