Kerry sees no sign of "seriousness of purpose" on part of Russia, which in turn terms US threat "emotional breakdown".
The US is "on the verge" of ending talks on Syria with Russia following days of deadly attacks on Aleppo, according to the US secretary of state.
US officials say the administration is looking at other ways to end the war in Syria that has been going on for over five years.
Speaking at the Atlantic Council think-tank on Thursday, John Kerry said that the US is "on the verge of suspending the discussion because it’s irrational in the context of the kind of bombing taking place".
He said the US has no indication of Russia’s "seriousness of purpose" and discussions made no sense at a time when Russian and Syrian warplanes were bombing rebel-held areas of Syria’s second largest city.
The US has been working with Russia for months to try to secure a ceasefire in Syria.
The latest truce collapsed last week after several days of relative calm.
The joint bombardment of Aleppo has left more than 400 people dead and at least 1,700 wounded since last week
On Wednesday, US officials told Reuters news agency that President Barack Obama’s government had begun to consider tougher responses - including military options - to President Bashar al-Assad government’s assault on Aleppo.
The officials said the failure of diplomacy in Syria has left the US administration no choice but to consider alternatives, most of which involve some use of force and have been examined before but held in abeyance.
Earlier, Sergei Ryabkov, Russia’s deputy foreign minister, said the US threat to suspend talks on Syria over the bombardment of Aleppo’s rebel-held areas constitutes "an emotional breakdown".
Ryabkov also rejected US calls for a week-long truce as "unacceptable", but said a two-day ceasefire could allow desperately needed aid to reach the more than 250,000 civilians trapped in Aleppo.
Al Jazeera’s Rory Challands, reporting from Moscow, said the Kremlin "saw the seven-day ceasefire as a step that would allow the terrorists, as they call them, to stock up on supplies and rest".
"They [the Russians] say that the US is fixated on demands of a seven-day pause for reasons only they know," he said.
"It seems after the negotiations that brought about the collapsed ceasefire - there is a widening gulf between the Russians and the Americans."
Ryabkov’s comments followed a previous warning by Kerry that the US would end talks on the conflict, as well as a military pact that involved targeting the ISIL and Jabhat Fateh al-Sham groups unless Russia halted the assault on Aleppo.
Kerry conveyed the message in a call to his Russian counterpart, Sergey Lavrov, on Wednesday in which he voiced "grave concern" over the Syrian government’s air and land attacks on Aleppo.
Kerry said the US held Russia responsible for the use of incendiary and bunker buster bombs which put Aleppo civilians at great risk, according to John Kirby, the State Department spokesperson.
The Syrian government’s offensive to recapture all of Aleppo - with Russian air support and Iranian help on the ground - has been accompanied by bombing that residents have described as unprecedented in its ferocity.
On Wednesday, at least six civilians were killed when air strikes hit two hospitals in rebel-controlled parts of Aleppo.
The M10 and M2 hospitals were hit before dawn, forcing both to shut temporarily, and leaving just two of east Aleppo’s eight hospitals with surgical facilities.
Al Jazeera’s Diplomatic Editor James Bays asked Bashar Jaafari, Syria’s UN ambassador, if his country had bombed the two hospitals.
Jaafari walked away laughing, without giving an answer.
"It’s not clear why he was laughing considering his country is being accused of war crimes in Aleppo," said our correspondent.
An estimated 250,000 people still live in eastern Aleppo, which has been under near-continuous siege since mid-July, causing food and fuel shortages.
Attacks on water installations from both sides have left more than two million civilians without water.
The Syrian civil war started as a largely unarmed uprising against Assad in March 2011, but quickly escalated into a full-blown armed conflict.
Five years on, more than 400,000 Syrians are estimated to have been killed, and almost 11 million Syrians - half the country’s prewar population - have been displaced from their homes.