The United States last month imposed sanctions on firms working on the almost-completed pipeline, which will double gas shipments to Germany and is a key part of Moscow's export strategy for state energy giant Gazprom.
Washington believes the 9.5-billion-euro (USD 10.6-billion) project will give Russia too much influence over security and economic issues in western Europe.
Putin said the US sanctions would cause delays of "several months", after Energy Minister Alexander Novak said in December that the pipeline would be finished by late this year.
Merkel added that "despite the sanctions it will be possible to complete Nord Stream 2... There is a certain delay but it will be completed."
She reiterated that Germany "considers extraterritorial sanctions to be unsuitable and that's why we continue to support this project."
Russia "could complete construction independently without using foreign partners," Putin said.
"It is a question of deadlines. That's the only issue here."
