Xi and Trump have agreed to hold bilateral talks focusing on the US-China trade war during the summit.
The crowdfunding campaign "Make the anti-extradition bill an issue for the G20 summit" aimed to raise HK$3 million (US$384,315) in two days to place a front-page open letter in the Financial Times, and if the funds are sufficient, on other worldwide newspapers, including New York Times, The Wall Street Journal and Japanese newspapers.
But Lam stopped short of protester demands to scrap the bill altogether, saying it would be suspended indefinitely.
Holding placards that said "Free Hong Kong from China colonisation" and "free Hong Kong, help Hong Kong", the protesters handed in their letters to representatives of the consulates.
Organizers are calling for a "silent march" in the city's business district on Wednesday - moving past consulates of the Group of 20 nations - an organization that meets later this week in Japan.
Opponents of the extradition bill fear it would put them at the mercy of Chinese courts, controlled by the Communist Party, with a record of arbitrary detentions, torture and other human rights violations.
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"Hong Kong is China's special administrative region".
Hong Kong returned to Chinese rule in 1997, since when it has been governed under a "one country, two systems" formula that allows freedoms not enjoyed in mainland China, including the freedom to protest and an independent judiciary.
However, Chinese assistant foreign minister Zhang Jun said on Monday that the G20 summit was a forum to focus on global economic issues and the Hong Kong situation would not be allowed to enter the discussion.
Many in Hong Kong accuse China of extensive meddling in its government - including obstruction of democratic reforms, interference with local elections and being behind the 2015 disappearance of five Hong Kong-based booksellers who specialised in works critical of Chinese leaders.
More than 22,000 people had raised HK$5.5 million within hours of the crowdfunding campaign's launch, exceeding a HK$3 million target. The group has called on people to turn out in force.
Opposition to the bill in Hong Kong has broadened into a tense struggle for greater democracy, with huge marches on June 9 and June 16 viewed as a stunning repudiation of the administration of the city's top official, the Beijing-backed Carrie Lam, who faces a no-confidence motion in the legislature Wednesday.