Lavrov's comments, made after a meeting of the Council of Europe human rights organisation in Vienna, suggested Moscow could be preparing a reason to question the legitimacy of the May 25 election if it is unhappy with the outcome.
"Holding elections at a time when the army is deployed against part of the population is quite unusual," he told a news conference in response to a question about whether Moscow would recognise the vote. "We will see how this process ends."
Lavrov said Ukraine should agree a new constitution to define presidential powers before people cast their ballots.
Russia annexed the Crimea from Ukraine in March and does not recognise the government that took power in February after Ukraine's pro-Moscow president was ousted.
The West accuses Moscow of trying to destabilise its fellow former Soviet republic by fomenting separatist unrest in the Russian-speaking east.
Unrest could also be used by Russia as grounds to withhold recognition of the election.
Russia denies the accusations and says the West and the new, pro-Europe authorities in Kiev have aggravated the crisis. Asked about a German proposal to hold a second international meeting on Ukraine, Lavrov said agreements reached during the first talks in Geneva had still not been implemented.
"Meeting in the same format, when the opposition to the current Ukrainian regime will be absent at the negotiating table, would hardly add anything," he said.
"One could possibly do it but we would be going round in circles, again saying that one needs to carry out what we had agreed on.
"And it's the Ukrainians who should deliver, both the regime and those opposing it."
Meanwhile, both sides have been burying their dead as Ukraine slides further towards war, with supporters of Russia and of a united Ukraine accusing each other of tearing the country apart.
The deadliest few days since the separatist uprising began have transformed the conflict, hardening positions and leaving little room for peaceful resolution.
In Kramatorsk, a separatist-held town in the east that saw an advance by Ukrainian troops at the weekend, the coffin of 21-year-old nurse Yulia Izotova was carried through streets stilled by barricades of tyres and tree trunks. Scattered red carnations traced the route.
At the Holy Trinity Church, seven priests led mourners in prayers for a woman killed by large calibre bullets, which the townsfolk say were fired by Ukrainian troops.
"They shoot at us. Why? Because we don't want to live with fascists?" asked 58-year-old passport photographer Sergei Fominsky, standing with his wife among the mourners. "We're not slaves. We kneel to no-one."
In Odessa, a previously peaceful, multi-ethnic Black Sea port, more than 40 people were killed on Friday in the worst day of violence since the February revolt toppled Ukraine's pro-Russian president.
Yesterday pall-bearers in the port carried the open casket of Andrey Biryukov from a van to the street corner where he had been fatally shot.