The US secretary of state has threatened Moscow with more economic sanctions if the ceasefire in eastern Ukraine is not being adhered to.

John Kerry cautioned on Monday that the truce between the Ukrainian government and pro-Russian rebels agreed last month was not being "fully" implemented.

Kerry said that there so far had been "a kind of cherry picking, a piecemeal selectivity to the application of the Minsk agreements.

"If there continue to be these broad swaths of non-compliance ... then there would be inevitably further consequences that would place further strain on Russia's already troubled economy," he said.

Kerry made the comments after meeting Russian Foreign Minister Sergey Lavrov in Geneva.

Lavrov, speaking separately, said the deal struck in Minsk, Belarus, on February 15 was on the right track.

He welcomed the "tangible progress" in the implementation of the peace deal, saying "the ceasefire is being consolidated, heavy weapons are withdrawn".

The Geneva meeting coincided with the release of a UN human rights report stating that the conflict has claimed at least 6,000 lives, with hundreds killed in the past few weeks alone.

The report also refers to "credible accounts" of heavy weapons and foreign fighters continuing to flow into eastern Ukraine from Russia.

Despite continued fighting on the ground, the leaders of Russia, Ukraine, France and Germany agreed on Monday that progress has been in made to create a ceasefire.

But according to the French presidency's statement on Monday, the leaders of the four countries, speaking over the phone, agreed that "the situation must be improved further" and that they would ask the Organisation for Security and Co-operation in Europe (OSCE) to play a bigger role in ensuring the ceasefire is implemented.

Source: Al Jazeera and agencies