Mr Trump said Germany was “totally controlled by Russia” because of the high level of natural gas it imported, and this was a “bad thing for Nato”.
Mrs Merkel hit back by insisting Germany was independent and defending its contribution to the alliance.
The last summit both leaders ended in acrimony in a row over trade.
They are due to meet again in Brussels on Wednesday.
The Brussels summit comes less than a week before Mr Trump is due to hold his first summit with Vladimir Putin, in Helsinki, reviving concerns among US allies over his proximity to the Russian president.
President Trump shocked some by quipping that the Nato summit might prove harder than next Monday’s summit with Mr Putin.
He has said the US is being “taken advantage of” by other members of the Nato alliance, which was set up in 1949 to counter the Soviet Union, of which Russia is the main successor state.
European Council President Donald Tusk accused him of criticising Europe “almost daily”, tweeting: “Dear America, appreciate your allies, after all you don’t have that many.”