The leaders have now gathered for an afternoon plenary session and have had their G20 joint photograph. Afterwards there will be any number of bilateral get-togethers on the sidelines.
Hopes of progress over tariffs in Mr Trump's expected talks with Chinese leader Xi Jinping have been dampened.
The two economic giants are locked in a trade war, which may possibly even escalate.
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World leaders are meeting in Argentina for their annual G20 summit amid new tension with Russia over Ukraine and a US trade row with China.
However, Mrs Merkel's own arrival at the summit has been delayed by a technical fault in her plane.
The plane was forced to land in Cologne on Thursday evening. She has resumed her journey but will not get to Buenos Aires until after other leaders have started their discussions.
