Russia says it will unilaterally start using force against those violating the partial truce in Syria, if the US does not agree to joint rules by Tuesday.
A Russian general said delays in agreeing the rules were "unacceptable" and proposed holding an urgent meeting.
However, the US rejected the call, saying Russia's concerns were already being handled in a constructive manner.
The cessation of hostilities has significantly reduced the violence in Syria since it began on 27 February.
However, both the Syrian government and opposition have complained of repeated violations.
Last week, Russia started pulling out most of its forces from Syria, saying it had largely achieved the goals of the air campaign it launched in September to bolster President Bashar al-Assad.
But it vowed to continue targeting the jihadist groups Islamic State (IS) and al-Nusra Front, which are excluded from the truce.
As part of the deal between the warring parties they brokered last month, the US and Russia agreed to chair a ceasefire taskforce that would "develop effective mechanisms to promote and monitor compliance with the ceasefire".
On Monday, Lt Gen Sergei Rudskoi, chief of the main operational directorate of the general staff of the Russian armed forces, said the US had not responded to repeated requests to draw up measures to tackle "groups that systematically violate" the truce.
The general claimed the US - which backs the opposition - was "not ready to have a substantive discussion".
"Delaying entry into force of co-ordinated rules of response to violations of the cessation of hostilities regime in Syria is unacceptable," he added.
Gen Rudskoi said Russian officials were ready to complete the work on the rules at a meeting in Moscow or any other location acceptable to their US counterparts.
"In the absence of US reaction to these proposals the Russian Federation will begin unilateral application of the rules provided under the agreement on 22 March," he warned.
A US official dismissed the comments, telling Reuters news agency: "We have seen the media reports on alleged Russian concerns over ceasefire violations.
"Whoever is making such statements must be misinformed, because these issues have been discussed at length already, and continue to be discussed, in a constructive manner."
The dispute comes as indirect peace talks in Geneva between the Syrian government and the main opposition umbrella group enter their second week.
Meanwhile, at least 26 pro-government fighters were killed fighting IS militants near the ancient city of Palmyra, according to the Syrian Observatory for Human Rights.
The UK-based group reported that they died as IS repelled a government offensive to the west of the Greco-Roman ruins, which are a Unesco World Heritage site.
Russian warplanes also bombed parts of the nearby town on Monday, it said.