US Secretary of State John Kerry says the US hopes the Ukraine ceasefire deal will be implemented within "hours".

But Kerry said he had warned Russia's foreign minister that his country faced "further consequences" if conditions were not met.

Speaking after their meeting, Sergei Lavrov told the UN there had been "tangible progress" with the truce.

Both Ukraine and the rebels say they are withdrawing heavy weapons from the front line under the Minsk ceasefire.

But tensions remain high with continued fighting in recent days shaking a fragile ceasefire that is otherwise said to be holding.

Monitors from the OSCE security group have reported weapons movements on both sides but say it is too early to confirm a full withdrawal.

Kerry said the ceasefire must be respected in all areas, implying that fresh sanctions could be implemented against Russia.

But he said he was optimistic the ceasefire would be in place fully in "hours, certainly not more than days".

"I'm very hopeful that it will in fact be the start of a change which would be an improvement for everybody," he told a news conference in Geneva.

Fighting began in Ukraine's eastern Donetsk and Luhansk regions last April, a month after Russia annexed the Crimea peninsula.

Kerry's meeting with Lavrov - the first since he accused Russia of lying about its role in Ukraine's war - coincided with the release of a UN human rights report.

The report states that the conflict has claimed at least 6,000 lives, with hundreds killed in the past few weeks alone, although it says that the real number of fatalities could be considerably higher.

UN High Commissioner for Human Rights Zeid Ra'ad Al Hussein said it painted a picture of "merciless devastation of civilian lives and infrastructure".

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

The Ukrainian government, Western leaders and Nato say there is clear evidence that Russia is helping the rebels with heavy weapons and soldiers - something Moscow denies.

Earlier Kerry called on the UN to examine rights violations.

Meanwhile Sergei Lavrov said weapons were being withdrawn from front lines.

The Russian FM called on the Ukrainian government to distance itself from "extremists" and urged Kiev to promote economic recovery of rebel-held areas.

He also described the brutal murder of Russian opposition politician Boris Nemtsov on Friday as a "heinous crime".

Nemtsov, who was shot on a bridge near the Kremlin, had been planning an anti-war rally and was said to be working on a report to expose the presence of Russian troops in Ukraine.

His allies accused the Kremlin of involvement but Lavrov condemned the murder and vowed that Russia would find the killers.

"This is a heinous crime which will be fully investigated within the full framework of the law to ensure the perpetrators are brought to justice."

Kerry was expected to use the talks to call for an investigation examining not only who pulled the trigger, but who ordered, funded and co-ordinated Nemtsov's murder.

Last week, Kerry had accused the Kremlin of "craven behaviour" in its support for the pro-Russian fighters last week.