They will hold a longer meeting later, and say they want to repair ties damaged by a crises including Russia’s alleged meddling in the US election.
Climate change and trade are set to dominate as the two-day summit opens, with mass protests in the streets.
Clashes at a “Welcome to Hell” rally left 76 police officers injured.
By choosing to hold the summit in Hamburg, Germany’s northern hi-tech powerhouse, Chancellor Angela Merkel is seeking to show mass protests can be tolerated in an open democracy, correspondents say.
The G20, or Group of Twenty, is a summit for 19 countries, both developed and developing, plus the EU.
The individual countries are Argentina, Australia, Brazil, Canada, China, France, Germany, India, Indonesia, Italy, Japan, Mexico, Russia, Saudi Arabia, South Africa, South Korea, Turkey, the UK and the US.
According to NBC News correspondent Peter Alexander, it is likely that only four other people will be present at the meeting: US Secretary of State Rex Tillerson, Russian Foreign Minister Sergei Lavrov and two interpreters.
It is unclear if they will speak to reporters afterwards or to what extent media will be admitted to the meeting. After phone calls between the leaders in January and May, the White House and Kremlin released summaries of the conversations.
What we do know is that the two men have staked out opposing views on major international issues in the run-up to the summit:
On Thursday, Mr Trump used a speech in the Polish capital Warsaw to call on Russia to stop “destabilising” Ukraine and other countries, and “join the community of responsible nations”
Setting out his own G20 agenda in German financial newspaper Handelsblatt, Mr Putin called for US-led sanctions, imposed in response to Russia’s annexation of Crimea in 2014, to be lifted on his country
Mr Putin also argued strongly in favour of the Paris climate agreement, saying it was a “secure basis for long-term climate regulation” and Russia wanted to make a “comprehensive contribution to its implementation”. President Trump, of course, has taken America out of the agreement.
While there was less mention of Syria, Washington supports some armed opposition groups, while Moscow is the main ally of President Bashar al-Assad, so the potential for a difference of opinion there too is high.