The meeting in Rome came after US lawmakers passed a bill - dubbed the Ukraine Freedom Support Act - calling for additional sanctions against Russia and the delivery of up to $350 million (€280 million) worth of US military hardware to Kiev.
"Undoubtedly, we will not be able to leave this without a response," deputy foreign minister Sergei Ryabkov told Interfax news agency ahead of the talks.
The Senate bill must still be approved by the White House, which has so far been reluctant to provide direct military assistance to Ukraine for fear of being drawn into a proxy war with Russia, which is backing separatist forces in Ukraine.
The legislation authorizes - but does not legally require - President Barack Obama to provide lethal and non-lethal military aid to Ukraine, including anti-tank weapons, ammunition and troop-operated surveillance drones.
State Department officials have insisted there are no plans to move beyond providing non-lethal supplies such as body armour and communications equipment.
US officials have stressed the main thrust of Kerry's pre-Christmas diplomatic whirl is a looming showdown at the UN on a bid for Palestinian statehood. But the conflicts in Ukraine and Syria would also figure high on the agenda.
"We have a number of critical issues to talk about," Kerry said, as he met with Lavrov in the splendour of the US ambassador's residence in Rome.
The talks between the two men went on for more than three hours, a senior State Department official said late on Sunday.
On Ukraine, the source said Kerry had "reiterated the importance of fully implementing the Minsk agreement and de-escalating the situation on the ground".
The Minsk agreement refers to a ceasefire deal agreed in the Belarus capital in September which has yet to be fully implemented.
US, Europe in 'lockstep'
In a flurry of meetings which will also take the top US diplomat to Paris and London, Kerry was planning to discuss how to "remain in lockstep" with European allies and the "pressure strategy that we've been using".
The eight-month-old conflict between government forces and pro-Russian separatists in eastern Ukraine has left at least 4,634 dead and 10,243 wounded, and displaced more than 1.1 million people, according to new UN figures.
The threat of fresh sanctions comes as Russia's economy crumbles under previous rounds of Western sanctions and a collapse in oil prices.
The Ukrainian army on Sunday reported 14 attacks on its positions in the past 24 hours, including one in which Grad rockets, mortars and anti-tank weapons were fired "as a provocation", but no one was killed or wounded.
Ukraine has been worried for months that the Russia-backed separatists will launch an offensive on the port of Mariupol to carve a land corridor between the Russian border and the Crimean peninsula, a Ukrainian region annexed by Moscow in March.
Ukraine announced on Friday it would bolster its army next year by conscripting another 40,000 soldiers, and doubling its military budget.
While the Russian economy has been hit hard by the conflict, the International Monetary Fund's number two David Lipton said Saturday he was "impressed" by Ukraine's plans for reform after lawmakers approved a government programme of severe austerity cuts.
The IMF this year granted Kiev $17 billion in financial aid over two years, as part of a $27 billion global rescue package set up by Western countries.