EU ambassadors have agreed to formally begin accession negotiations with Ukraine and Moldova later this month.
The Belgian EU presidency said talks would start on 25 June.
According to the presidency, the decision should be given the nod by finance and economy ministers at a meeting next Friday.
G7 nations have reaffirmed their commitment to support Ukraine "for as long as it takes".
A final statement from the summit in Italy saw leaders affirm their plan to finance a $50bn loan for Kyiv using "extraordinary revenues" from frozen Russian assets.
They said the move sends an "unmistakable signal" to Vladimir Putin as the war rages on.
Volodydmyr Zelenskyy called the decision a" vital step forward in providing sustainable support for Ukraine in winning this war".
Mr Putin, meanwhile, has condemned the freezing of Russian assets as "theft" and has vowed it "will not go unpunished".
According to US and French officials, the money could be in Kyiv's hands before the end of the year.
