Blinken said that the US seeks "a predictable, stable relationship with Russia" in comments ahead of the meeting, according to a State Department transcript, DPA news agency reported.
But he also said "it's no secret that we have our differences" before the meeting, which was held on the margins of an Arctic Council ministerial meeting.
"When it comes to those differences," Blinken said, US President Joe Biden has let his Russian counterpart Vladimir Putin know that "if Russia acts aggressively against us, our partners, our allies, we'll respond."
Lavrov responded by saying that the two countries "greatly diverge when it comes to our assessment of the international situation and our approaches towards how we should resolve it."
"We are prepared to discuss all issues on the table with the understanding that our discussions will be honest, factual, and with mutual respect," the Russian minister said during the meeting on Wednesday.
The top diplomats were expected to discuss a potential meeting between Biden and Russian President Vladimir Putin. Biden has suggested a summit in a third country, but it is unclear whether Putin will say yes.
Other topics for Lavrov and Blinken's talks included the escalation in the Israeli-Palestinian conflict, North Korea's and Iran's nuclear programmes and the situation in Afghanistan.