The nation's top diplomat, in an interview with CNN's Elise Labott, said, "We have made it crystal clear to Russia to what the consequences might be. The President, myself, we've had conversations, we know what's happening, we are being vigilant."
Concerns about hacking into US election systems have heightened in the wake of digital break-ins to Democratic campaign organizations, which federal authorities have linked to Russian intelligence services.
"I do not believe Russia will have the ability to effect this election and we are going to be absolutely vigilant about it," Kerry said. "The President has made that clear and Russia is warned."
Kerry, the 2004 Democratic presidential nominee, also recalled the exhilaration and exhaustion of a national campaign's final stretch.
"Right now you're getting into October. October is the month when your juices, your blood really begins to flow. You're down to 30 days," said the former Massachusetts senator. "You've been at this for two years plus whatever it is. Uh, it's exhausting but you can see the end, the stakes really descend on you. You really have a sense of just how much is up for grabs here in terms of the future of our nation. And I think that energizes, that clarifies the focus, it provides an intensity and a passion. And I'm confident that over the next month we will see a sharpening, if you will, of the differences of the arguments between the candidates."
But Kerry declined to weigh in on specifics of the tight race between Hillary Clinton, his predecessor at Foggy Bottom, and Republican nominee Donald Trump.
In the interview Kerry was also sharply critical of Russia for failing to enforce a ceasefire agreement in Syria, calling on Russia to "stop the grandstanding, stop the showboating and get the humanitarian assistance going."
Kerry's comments come as convoys carrying humanitarian aid are blocked from reaching some of Syria's hardest-hit areas.
"It is now Sunday morning. This started Monday night of last week -- this past week. And the humanitarian assistance is supposed to be flowing," Kerry said.
He pinned the blame on Syrian President Bashar al-Assad, who is at war with insurgents. The United States and Russia are split on who they back in the Syrian civil war, but are attempting to work together to combat terror groups in the country.
Kerry complained that Assad's government is blocking the aid and has continued the violence, and said Russia must pressure Assad.
"The regime, once again, is blocking it. So Russia's client, Russia's supported friend, is the single biggest blockade to the ability to move forward here," Kerry said.
"So let me just say this clearly: Russia signed up to a cessation of hostilities. Assad said he would live by it. Then he needs to stop and let the joint implementation center get set up so Russia and the United States can coordinate in order to avoid the kind of terrible thing that happened yesterday that we all acknowledge and regret," Kerry said.
His comments come the day after the US-led coalition fighting ISIS admitted it struck Syrian forces rather than a terror target.
Kerry also issued a broader call for Russia to pressure Assad.
"The biggest judgment they need to make is to stop Assad from bombing people indiscriminately, which he continues to do," the secretary of state said.
"And if you are serious about having a ceasefire, and they say they are, then they should keep Assad from flying right now and prove their sincerity about a ceasefire," he said. "But to allow Assad -- who is a spoiler; he doesn't want a ceasefire -- to allow him to continue to go after opposition, pretending that they are Nusra, is in and of itself a huge challenge to this effort."
Kerry said "there are no good options" to stop the crisis in Syria, and that the options that do exist are "ugly."
"One option is trying to move toward a ceasefire and trying to get to the table to have a negotiation. But the other option moves to more arms in the area, more fighting, more destruction, more migrants, more refugees. More children, women, schools, hospitals hit. Literally, possibly the destruction of Syria as an entire nation and state. And it is getting close to that even now," Kerry said. "So the options are not pretty. But you've got to put to test the seriousness of purpose of a nation."
He acknowledged that Defense Secretary Ash Carter and others at the Pentagon have expressed reservations about a ceasefire agreement and in trusting Russia to help enforce it.
"Nothing in this agreement is based on trust," he said. "It is based on very specific steps that each side has to take. And that includes pulling back from this key access road in the north near Aleppo. It includes restraining both sides, Assad, and for us, the opposition, from engaging. And then it includes the delivery of humanitarian assistance, and delivering a real cessation of hostilities."
Kerry also weighed in on the explosion Saturday night in New York City, saying "the security in the city of New York will be unparalleled as it always is" in the wake of the incident.
"I'm not concerned about that. But I think we need to be concerned for every American and for the folks in New York on a day-to-day basis. Understand what's going on. The teams are doing that and as I said, they could not be more qualified or capable," he said.