Washington meanwhile is planning to send Ukraine sophisticated anti-aircraft missiles, US National Security Advisor Jake Sullivan told reporters, responding to a long-standing request from Zelensky for more advanced weapons.
The summit of the G7 -- which comprises Britain, Canada, France, Germany, Italy, Japan and the United States -- ends on Tuesday.
It will immediately be followed by a meeting of NATO countries in Spain, where Ukraine is again expected to dominate the agenda.
NATO said on Monday the military alliance would boost its high readiness force from 40,000 to 300,000 troops and send more heavy weaponry to its eastern flank following Russia's invasion of Ukraine.
NATO Secretary General Jens Stoltenberg called it "the biggest overhaul of our collective defence and deterrence since the Cold War".
Since failing to capture Kyiv early in the war, Russian troops have focused on the eastern Donbas region, where they have been gaining ground.
Two women had been killed by Russian bombardments in the northeastern Kharkiv region over the past 24 hours, a local official said on Monday.
Russian shelling also continued in and around the eastern city of Lysychansk, after Russian forces at the weekend took full control of its twin city, the industrial hub Severodonetsk, following weeks of fierce fighting.
"Lysychansk and nearby villages are living their toughest days. Russians destroy everything on their way," said Lugansk regional governor Sergiy Gaiday.
Taking Lysychansk would give Russia control of the entire Lugansk region of the Donbas.
Kyiv meanwhile was reeling from the first Russian strikes on the capital in three weeks. A missile struck a residential building early on Sunday, Ukraine said, leaving one person dead.
Russia denied it had hit a civilian target, however, saying its forces had struck a weapons factory in the neighbourhood.
Zelensky stressed on Monday that "now is not the time for negotiations" with Russia because Kyiv is still seeking to consolidate its positions, a French official said.
Gold, oil, debt
Sweeping Western sanctions designed to choke off Moscow's access to the international financial system have pushed Russia closer to its first foreign debt default in a century.
Russia said on Monday two of its debt payments were prevented from reaching creditors after a key deadline expired.
But "there are no grounds to call this situation a default", Kremlin spokesman Dmitry Peskov said.
G7 members said they were paving the way for further sanctions aimed at depleting Putin's war chest, while minimising the blowback on their own economies.
After kicking off their gathering on Sunday with a plan to ban imports of Russian gold, the G7 had also made progress in talks on a price cap on Russian oil, a senior US official said on Monday.
The cap has the twin goals of starving the Kremlin of a key revenue stream and forcing down the price of Russian oil in the hope of reining in inflation, the official said.
Zelensky has urged the G7 to push through the measure but European officials fear it will be difficult to implement and say more discussions are needed.
To help bring down surging crude prices, France urged oil-producing nations to raise output in an "exceptional manner".
In another effort to punish Russia and help Ukraine, the G7 plans new measures designed to hamper Russia's ability to resupply its weaponry, a senior US official said.
The leaders likewise share the view that money collected from higher trade tariffs imposed on Russian exports should be funnelled as aid to Ukraine "to ensure that Russia pays for the cost of its war", the official added.
One of the most worrying spillover effects of the war has been the threat of food shortages in vulnerable countries, especially in Africa, as Russia's blockade of key ports holds up vital Ukrainian cereal exports.
"We urgently call on Russia to ... enable free passage of agricultural shipping from Ukrainian ports in the Black Sea," G7 leaders said.
Russia denies being responsible for the delivery disruptions and says Western sanctions are to blame.
Non-G7 countries Argentina, India, Indonesia, Senegal and South Africa have also joined the summit in Elmau Castle, Bavaria.
Indonesian president Joko Widodo is slated to host the G20 summit in November and has shrugged off Western pressure to exclude Putin from the gathering.
Scholz on Monday said he was open to still attending the G20.
Putin meanwhile is scheduled to travel to Tajikistan and Turkmenistan this week, his first forays abroad since the invasion.