Kerry and Netanyahu spoke at a joint news conference in Jerusalem after the two met Monday night.
"I think it's fair to say that we made progress, that we were pleased with the substance of the discussion and agreed, each of us, to do some homework," Kerry said. "And we're going to do our homework over the course of the next weeks, and today we're going to continue some of that discussion with a view to seeing how we can really pull all of the pieces together and make some progress here."
Negotiations between Israel and the Palestinians have been mostly moribund for more than four years, with neither side indicating a willingness to drop objections or preconditions before resuming negotiations.
Netanyahu said he was determined not only "to resume the peace process with the Palestinians but to make a serious effort to end this conflict once and for all."
"This has economic components," Netanyahu said. "But it also has a political component -- political discussions that will address a myriad of issues. Foremost in our minds are questions of recognition and security."
Kerry said the economics "in no way" substitute for the political track but are "in addition to" the political court. "The political track is first and foremost; other things may happen to supplement it," he said.
Netanyahu said he and Kerry discussed several other issues but singled out talks on Syria and Iran.
Concerning Syria and its two-year civil war, the prime minister said, "[The] fragmentation of that country is creating a situation where one of the most dangerous stockpiles of weapons in the world is now becoming accessible to terrorists of every shade and hue. This is of great concern for both of us, for both the United States and Israel, and we are talking about addressing this problem specifically."
On Iran, Netanyahu said "everybody" understands that Iran is running out of time to tamp down its nuclear aspirations.
"I think we ... understand what it means for the world to have rogue states with nuclear weapons," he said. "Iran cannot be allowed to cross into that world. It cannot be allowed to continue its program, its nuclear weapons program, and we must not allow it to continue to do so in defiance of the entire international community."
Kerry reiterated President Obama isn't bluffing when he says Iran can't and won't have a nuclear weapon.
"And the United States of America has made clear that we stand not just with Israel but with the entire international community in making it clear that we are serious, we are open to negotiation, but it is not an open-ended, endless negotiation," Kerry said. "It cannot be used as an excuse for other efforts to try to break out with respect to a nuclear weapon. ... [We] hope the Iranians will come back to the table with a very serious proposal."
Notable deaths of 2014 [PHOTOS]