The US secretary of state said Lavrov shared new ideas on resolving the conflict which he promised to present to US President Donald Trump, but played down the prospect of a breakthrough.
The pair met hours after Moscow pummeled Kyiv for a second straight night and as the United Nations said the number of victims from Russian attacks was at its highest level in three years.
Trump, who forced the warring countries to open negotiations for the first time in three years, this week accused Russian President Vladimir Putin of talking "bullshit" on Ukraine.
The US leader's efforts to secure a ceasefire have failed to extract any concessions from the Kremlin, despite multiple calls with Putin.
Rubio told reporters Lavrov had floated something "new" on the conflict, but did not give details.
"It's not a new approach. It's a new idea or a new concept that I'll take back to the president to discuss," he said.
He added that it was not something that "automatically leads to peace, but it could potentially open the door to a path."
The US diplomat said he had also conveyed Trump's anger that the more than three-year war, triggered by Russia's 2022 invasion, was still ongoing, criticising Moscow's lack of "flexibility".
Ukrainian President Volodymyr Zelensky said that the United States would deliver more weapons to Kyiv and that he had "specific dates" on when they would arrive, in response to an AFP question.
- 'Large defense package' -
Zelensky said in an X post that Ukraine was "ready" for different approaches to "scale up protection", including by "purchasing a large defense package from the United States, jointly with Europe".
Trump seemed to back up such an agreement. In an interview with American broadcaster NBC late on Thursday, he said NATO was "paying" the United States for weapons to send to Ukraine.
"We're sending weapons to NATO, and NATO is paying for those weapons, 100%... And then NATO is going to be giving those weapons (to Ukraine)," Trump said.
Trump also said he would make a "major statement... on Russia" on Monday.
NATO secretary general Mark Rutte said he had spoken with Trump and was "working closely with allies to get Ukraine the help they need".
The leaders of Britain and France meanwhile announced they had prepared plans for a peacekeeping force to be deployed to Ukraine in the event of a ceasefire.
- 'Terror' -
The Kremlin denied peace talks were stalled and said it was still open to contacts.
Moscow has for months refused a ceasefire and two rounds of talks with Ukraine have produced no breakthrough.
The Ukrainian air force said Russia launched 415 drones and missiles at the country while Zelensky urged allies to quickly roll out fresh sanctions against Moscow.
The fresh onslaught came just one night after Russia fired a record 741 long-range drones and missiles.
Officials said the nighttime attack on Kyiv also wounded 22 people.
AFP reporters saw firefighters putting out flames in a damaged residential building and people emerging from shelters, carrying sleeping mats and pets after the air alert was lifted.
Russia's defence ministry said the strike targeted "military-industrial enterprises" in Kyiv as well as airbases.
The UN announced that attacks on Ukrainian cities in June had led to a three-year high in the number of civilians killed or wounded, reports BSS.
It said it had verified at least 232 people killed and 1,343 wounded during the month -- the highest combined toll since April 2022.