"I think it's a new and a different approach," Rubio told reporters after talks with Russian Foreign Minister Sergey Lavrov.
"I wouldn't characterise it as something that guarantees a peace but it's a concept that, you know, that I'll take back to the president".
He did not elaborate.
Rubio added that US President Donald Trump has been "disappointed and frustrated that there's not been more flexibility on the Russian side" to bring about an end to the conflict.
"We need to see a roadmap moving forward about how this conflict can conclude. And then we shared some ideas about what that might look like," he said of the 50-minute meeting.
"We're going to continue to stay involved where we see opportunities to make a difference."
In a statement released shortly after Thursday's meeting, Russia's foreign ministry said that "substantive and frank exchange of views" had taken place on issues including Ukraine, Iran, Syria and other global problems.
"Both countries reaffirmed their mutual commitment to finding peaceful solutions to conflicts, restoring Russian-American economic and humanitarian co-operation, and unimpeded contact between the societies of the two countries, something which could be facilitated by resuming direct air traffic," the statement said.
"The importance of further work to normalise bilateral diplomatic relations was also emphasised."
The two men held talks in Kuala Lumpur on the sidelines of the annual Association of Southeast Asian Nations Regional Forum, which brings together 10 ASEAN members and their most important diplomatic partners including Russia, China, Japan, South Korea, European countries and the US.
Hundreds of Russian drones and more than a dozen missiles targeted Kyiv and other Ukrainian regions in a second massive air attack in two days earlier on Thursday.
Ukrainian President Volodymyr Zelenskiy, who met allies in Rome to lobby for critical weapons and investment, said the attack on Thursday had involved about 400 drones and 18 missiles, primarily targeting the capital.
Local authorities said two people were killed, 23 were wounded and damage reported in nearly every district of Kyiv.
Explosions and anti-aircraft machine gun fire rattled the city.Â
Windows were blown out, facades ravaged and cars burned to shells, including in the city centre where an apartment in an eight-storey building was engulfed in flames.
"This is terror because it happens every night when people are asleep," said Karyna Volf, a 25-year-old Kyiv resident who rushed out of her apartment moments before shards of glass showered her home.
Ukrainian air defences stopped all but a few dozen of the drones, authorities said, a day after Russia launched a record 728 drones at Ukraine.
Escalating Russian strikes in recent weeks have strained Ukraine's air defences at a time when its troops are facing renewed pressure on the front line, and forced residents in Kyiv and across the country to seek cover in bomb shelters.
"Residential buildings, vehicles, warehouse facilities, offices and non-residential buildings are on fire," Tymur Tkachenko, head of Kyiv's military administration, said on the Telegram messaging app.
Russia's defence ministry said it had hit "military-industrial" targets in Kyiv as well as military airfields.
with AP
10°C