"I don't feel that... it properly represents what's going on in the world. It's a very outdated group of countries," Mr Trump said on Saturday.
The G7 group, which the US hosts this year, includes Canada, France, Germany, Italy, Japan and the UK.
The president said Russia, South Korea, Australia and India should be invited.
Speaking to reporters on board the presidential plane Air Force One, Mr Trump said that he was delaying the summit - which was scheduled to take place later in June - until September.
Last week, Mr Trump said it might be possible to hold a gathering at the White House and potentially parts of Camp David, the US presidential country retreat, despite concerns over the coronavirus pandemic.
German Chancellor Angela Merkel later rejected the president's invitation to attend a summit in person because of the outbreak.
Her spokesman thanked Mr Trump, but said the German leader "cannot agree to her personal participation, to a journey to Washington".
On Friday, UK Prime Minister Boris Johnson "agreed on the importance of convening the G7 in person in the near future" following a conversation with the US president, the White House said in a statement.
The G7 - or Group of Seven - leaders were scheduled to meet by videoconference in June in response to Covid-19.
The group is made up of the seven of the world's largest economies.
It regards itself as "a community of values", with freedom and human rights, democracy and the rule of law, and prosperity and sustainable development as its key principles.