The Ukrainian leader addressed the conference in Bavaria by video. He has demanded more arms and financial aid, and more sanctions against Russia.
Ukrainian President Volodymyr Zelenskyy has urged G7 leaders "to do everything possible" to end the war in his country by the end of the year, G7 sources said.
Addressing their summit in Bavaria by video link, Ukraine's leader appealed directly to the leaders for more help for his country, and for "intensified sanctions" against Russia.
It came as G7 leaders pledged to continue to support Ukraine in the long term.
Zelenskyy "had a very strong message that we must do everything possible to try to end this war before the end of the year," the sources said. He also stressed the importance of "not lowering the pressure and continuing to sanction Russia massively, heavily".
The West has already adopted several packages of measures since the start of the Russian offensive on Ukraine on 24 February.
During his speech, the Ukrainian president "spoke of the harshness of winter" in Ukraine "where it is more difficult to fight".
"At the end of the year, we will enter a situation where positions will be frozen," the sources said.
According to a European official quoted by Reuters, Zelenskyy also called for anti-aircraft defence systems, security guarantees, as well as help to export grain from Ukraine and for reconstruction aid.
G7 support for Ukraine 'as long as needed'
The G7 leaders pledged on Monday to "continue to provide financial, humanitarian, military and diplomatic support" to Ukraine "for as long as needed", in a joint statement issued at their summit in southern Germany.
They also expressed "deep concern" after Russia announced that it might transfer nuclear-capable missiles to Belarus.
An agreement is reportedly due to pursue a price cap on Russian oil, raise tariffs on Russian goods and impose new sanctions on hundreds of officials and entities supporting the war.
US President Joe Biden is expected to announce that Washington is providing an advanced surface-to-air missile system to Ukraine, as well as additional artillery support.
The Ukrainian leader's appeal comes the day after Russian strikes on Kyiv and elsewhere in Ukraine, denounced by Biden as acts of "barbarism".
"The G7 leaders (...) have enough joint potential to stop Russian aggression," Zelenskyy said in an earlier video message to his nation on Sunday evening.
"But this will only be possible when we get everything we ask for and in the necessary timeframe: arms, and financial support, and sanctions against Russia."
The Russian airstrikes over the weekend have been interpreted by Ukrainian and Western officials as a message of defiance aimed at the G7 and NATO, ahead of a summit of the military alliance beginning in Madrid on Tuesday.
Embargo on Russian gold
On the first day of their talks on Sunday at the castle, the seven industrialised countries (Germany, France, the United States, Canada, Japan, Italy and the United Kingdom) announced that they were broadening the sanctions against Moscow by declaring an embargo on gold newly mined in Russia.
This measure will hit "Russian oligarchs directly and attack the heart of Putin's war machine", said British Prime Minister Boris Johnson, while the West has already adopted several salvos of sanctions against Russia.
For German Chancellor Olaf Scholz, host of the Elmau summit, the bombing was another reminder that "it was right to be united and to support Ukraine".
Scholz said last week that he wanted to discuss the outlines of a "Marshall Plan" for Ukraine, referring to the US-sponsored plan that helped revive European economies after World War II. He added that "rebuilding Ukraine will be a task for generations".
There have been more calls among the G7 leaders for unity against Russia. Joe Biden said Russian President Vladimir Putin "has been counting on, from the beginning, that somehow NATO and the G7 would splinter, but we haven’t and we’re not going to". Boris Johnson, meanwhile, warned the leaders not to give in to "fatigue".
Meanwhile, Turkish President Recep Tayyip Erdogan will meet leaders from Finland and Sweden in Madrid on Tuesday to discuss the two countries' NATO applications — which have been blocked by Ankara — according to Helsinki.
This first high-level meeting with Finnish President Sauli Niinistö and Swedish Prime Minister Magdalena Andersson will take place in the presence of NATO Secretary-General Jens Stoltenberg, the Finnish presidency said on Twitter.
Russia intensifies attacks over weekend
For the first time in weeks, the Ukrainian capital was hit by Russian missiles on Sunday morning as fierce fighting continued in the east of the country in the deadly conflict now in its fifth month.
"One man was killed, he was only 37 years old. There are wounded, including a girl called Genya, she is seven years old and she is the daughter of the deceased (...) Her mother was also wounded. She is a Russian citizen. Nothing threatened her in our state, she was safe until Russia decided that everything in Ukraine is hostile to her," Zelenskyy said in his Sunday evening address.
Later, a local official reported a second death in Kyiv, telling the Unian news agency that a railway worker was killed and several others injured in the attacks while servicing rail infrastructure.
Zelenskyy said some of an estimated 14 Russian missiles launched at the capital had been intercepted, saying all those involved would be held responsible.
In the eastern Donbas region, there were intense airstrikes on Lysychansk, after a Ukrainian military chief said neighbouring Sievierodonetsk had been "fully occupied" by Russia's forces on Saturday.
Threat of global food crisis
The three-day G7 summit is largely devoted to the war in Ukraine and its aftermath.
Among the most urgent is the food crisis that threatens part of the planet as thousands of tons of grain lie dormant in Ukrainian silos due to the blockade or the occupation of Black Sea ports by the Russians.
Boris Johnson is to call on Monday for "urgent action" to revive Ukraine's vital grain exports at a time when poorer countries are on the brink of collapse, Downing Street has said.
The serious threat to many emerging countries will also be at the heart of Monday's talks between the heads of state and government and UN Secretary General Antonio Guterres, as well as the leaders of the five countries invited to Bavaria this year (India, Argentina, Senegal, Indonesia and South Africa).
India, Senegal and South Africa abstained from voting on a UN resolution condemning Russia's invasion of Ukraine.
Indonesian leader and G20 president Joko Widodo is also due to visit Ukraine and Russia soon to discuss the economic and humanitarian consequences of the Russian invasion.
Emerging economies are particularly exposed to the risk of food shortages and the climate crisis, another emergency that the seven leaders are expected to address with their guests.
Against a backdrop of Russian gas shortages, environmental NGOs fear that the G7 will backtrack on its commitments to end international funding for fossil fuels.