Finalizing the disengagement of fighting forces in Ukraine and keeping Kiev from renewing hostilities are the priorities for tackling the crisis, Russian Foreign Minister Sergey Lavrov has told his American counterpart, John Kerry, in Beijing.

Lavrov met the Secretary of State on the sidelines of the Asia-Pacific Economic Cooperation forum, which will bring President Vladimir Putin and his US counterpart, Barack Obama, together to discuss Ukraine for the first time since their informal conversation in Normandy, France, at D-Day anniversary commemorations in June.

“We believe it necessary to complete as soon as possible the settlement of the disengagement line so that the ceasefire and terms of the armistice could be monitored,” Lavrov said after his meeting with Kerry.

The disengagement is part of the so-called Minsk agreement, a semi-formal deal signed in early September that set out a roadmap for de-escalating the hostilities in eastern Ukraine, but failed to produce a full end to violence.

Lavrov said both the Minsk agreement and the earlier Geneva agreement, signed in April, which provides for Ukraine to hold profound constitutional reforms to address the grievances of its rebel provinces, must be implemented.

“John Kerry and I agreed today that this task is still relevant and probably even more acute than it was back in April, when the process was supposed to be launched,” he said.

#Lavrov's meeting with State Secretary John Kerry/ Встреча С.Лаврова с Госсекретарем США Дж.Керри в Пекине pic.twitter.com/Dis7Vhh9QL — MFA Russia (@mfa_russia) November 8, 2014

Moscow also asked Washington to put pressure on Ukrainian authorities in Kiev to prevent a possible resumption of its military crackdown on the rebels.

“The most important thing is not to indulge the ideas floating around in Kiev that they need to gather strength and go back to the use of force as a solution to the crisis, to talk hotheads out of such ideas and to make sure that the authorities in Kiev deliver on the promises they made, that is to pursue the path of political resolution,” Lavrov said.

The two also discussed the latest claims by Ukraine, which accused Russia of sending dozens of tanks and other military hardware to the rebel-controlled areas. The reports were not substantiated by any proof, while both the US and NATO said they had no evidence of such an incursion.

READ MORE: US, NATO say no evidence of new 'Russian invasion' of Ukraine

"Suffice it to say that 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. We have also agreed this is a dialogue between us that will continue," Kerry said.

Kerry also seemed to suggest that new Western sanctions against Russia were not imminent.

"The choices Russia makes will decide what happens with respect to sanctions in the long run here," Kerry said.

Earlier, Washington had threatened to impose a new round of sanctions, if Moscow acknowledged the election in the self-proclaimed Donetsk and Lugansk People’s Republics held last week. Russia declared its respect for the voice of the people the ballots represented, but stopped short of formally acknowledging them.

Lavrov and Kerry discussed other issues of interest to the US and Russia apart from the Ukrainian debacle, including the crisis in Syria and nuclear talks with Iran.