The US wants independent observers in the flashpoint region of Crimea and direct talks between Kiev and Moscow.
Russia is likely to call for greater representation for Ukraine's Russian-speaking areas in the Kiev government.
Meanwhile, the EU has offered 11bn euro ($15bn; £9bn) in aid to Ukraine.
European Commission President Jose Manuel Barroso said the package of loans and grants over the next couple of years is "designed to assist a committed, inclusive and reforms-oriented government" in Kiev.
Ukraine's finance ministry has predicted it needs $35bn to rescue its economy.
In other developments in Ukraine:
The national flag is once again flying over the administrative headquarters in Donetsk, replacing the Russian flag hoisted there five days ago. The building was evacuated after an apparent bomb threat
In Crimea, pro-Russian demonstrators have turned away families bringing food and supplies to Ukrainian troops refusing to surrender their bases
There are unconfirmed reports that Russian forces have seized two Ukrainian missile-defence sites in Crimea
'Bad example'
Mr Lavrov is expected to meet Mr Kerry and EU leaders on the sidelines of a long-planned conference on Lebanon in Paris.
Nato and Russia are also due to hold parallel talks in Brussels.
The Paris gathering is being seen above all as a chance to test the waters for a dialogue about Ukraine, says the BBC's diplomatic correspondent Bridget Kendall.
But UK Foreign Secretary William Hague said the Russians had already failed to appear at one meeting with the Ukrainians in Paris so he was "not optimistic" of making progress later.
"If we cannot make progress on that course there will be costs and consequences," he added, in reference to a threat of sanctions by the US and EU.
"It will be a test this afternoon of whether Russia is prepared to sit down with Ukraine."
Troops believed to be Russian servicemen are in control of Ukrainian military bases in Crimea
Mourners at Kiev's Independence Square remember the 88 protesters who died in clashes with police
Donetsk's regional government headquarters was emptied of pro-Russian activists
Earlier, Mr Lavrov underlined Moscow's differences with Western nations, accusing them of setting a bad example by supporting protesters - some of whom now make up the government - in their "armed coup d'etat".
But he did stress that Russia would "not allow bloodshed", adding: "We will not allow attempts against the lives and wellbeing of those who live in Ukraine and Russian citizens who live in Ukraine."
Mr Lavrov, speaking in Madrid after talks with Spain's foreign minister, also said it was up to the people of Ukraine and Crimea to decide if they wanted international monitors.
The Organisation for Security and Co-operation in Europe (OSCE) later confirmed that it had sent 35 unarmed military monitors - from 18 European countries - to Ukraine in response to a request from Kiev. It was not clear if they would be deployed to Crimea.
Mr Lavrov also insisted Moscow had no power to remove what it calls "self-defence forces" currently guarding key sites in Crimea, explaining that they were not Russian troops.
Personnel from the Russian Navy's Black Sea Fleet - which is based at the Crimean port city of Sevastopol - were in their normal positions, he added, while admitting Moscow had taken "additional special steps to raise awareness and tighten security" at its base.
While visiting Kiev on Tuesday, Mr Kerry condemned what he called Russia's "act of aggression" and praised the "restraint" of Ukraine's interim government.
He has said he wants to see the crisis managed through international institutions such as the OSCE.
Moscow has been calling for a return to an agreement reached on 21 February with the then President Viktor Yanukovych and the opposition.
This agreement included constitutional reform that would fully take into account the interests of all regions of Ukraine - giving the Russian-speaking areas in the east more influence and greater legal protection.
This, says the BBC's Richard Galpin in Moscow, would give Russia more leverage over the future direction of Ukraine.
Moscow has strongly condemned the recent change of government in Ukraine, which came after months of street protests, more than 90 deaths and the flight of President Yanukovych, a Russian ally.
Since his fall, Moscow has retained de facto control of Ukraine's southern autonomous region of Crimea.
Pro-Russian troops in unmarked uniforms began taking control of strategic points on Saturday.
Troops are surrounding Ukrainian military bases and other installations, while two Ukrainian warships are reported to be blocked by a Russian ship in Sevastopol's harbour.
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