To that end, he cited the jailing of the Russian opposition leader Aleksei A. Navalny, and the detentions of two Americans in Russia.
Mr. Biden also offered a warning on cyberattacks.
“I pointed out to him: We have significant cyber-capabilities — and he knows it,” the president said.
There were echoes of Helsinki and Mr. Trump’s professions of trust in Mr. Putin in an exchange between Mr. Biden and a reporter.
“Now that you’ve talked to him,” Mr. Biden was asked, “do you believe you can trust him?”
“Look,” the president replied, “this is not about trust. This is about self-interest and verification of self-interest.”
It is too soon to know how Mr. Biden’s summit will be received by the general public.
For Mr. Trump, the chummy public appearance with Mr. Putin in Helsinki was seen as damaging. (The same was true a year later, when the two men had an equally amiable meeting in Osaka, Japan, and Mr. Trump offered Mr. Putin a jocular warning at a news conference: “Don’t meddle in the election, President.”)
If Mr. Trump regrets it, there was no sign of it this week as the Geneva summit approached.
In a statement issued as Mr. Biden headed to Europe, Mr. Trump called his meeting with Mr. Putin “great and very productive,” and he defended supporting the Russian president over U.S. officials.
“As to who do I trust, they asked, Russia or our ‘Intelligence’ from the Obama era,” he said, then added: “The answer, after all that has been found out and written, should be obvious. Our government has rarely had such lowlifes as these working for it.”