The self-declared republics of Donetsk and Luhansk plan to elect regional leaders and parliaments on Sunday.
Moscow has already said it intends to recognise the result of the ballot.
Ukrainian President Petro Poroshenko argues that the polls threaten the peace process with Kiev.
Ukrainian troops have been battling the pro-Russian rebels in the east.
At least 3,700 people have been killed in the fighting, and many more have fled to other parts of Ukraine or to Russia.
A shaky truce took effect on 5 September, but there have been many violations and the situation remains volatile.
At a news conference in the Canadian city of Ottawa, Mr Kerry said the Ukrainian people had made a bold and clear choice for democracy when they voted in a parliamentary election last Sunday.
Turning to the planned rebel-run polls in the east, he said: "This would be a clear violation of the commitments made by both Russia and the separatists that it backs in the Minsk agreements.
"The United States along with the rest of international community will not recognise so called separatist elections unless they happen within the framework of the special status law passed by Ukraine's parliament and signed by President Poroshenko."
In last Sunday's Kiev-run polls, voting did not take place in rebel-held eastern districts, or in Crimea, which Russia annexed in March.
Following the polls, the pro-Western parties of President Poroshenko and Prime Minister Arseniy Yatseniuk are expected to form a coalition government.
Russia's Foreign Minister Sergei Lavrov said elections in the Donetsk and Luhansk regions "will be important to legitimise the authorities there".
"We expect the elections will go ahead as agreed, and we will of course recognise the results," he said.
Russian role In 2008 Russia also backed pro-Russian separatists in Georgia and later recognised the breakaway regions as independent.
Under the truce deal the Ukrainian authorities pledged not to prosecute the leaders of the eastern rebellion - yet many Ukrainian politicians want prosecutions, denouncing the rebels as "terrorists".
The deal also called for a withdrawal of "illegal militant groups" from Ukraine, but the rebels remain heavily armed and it is not clear how many Russian "volunteer" soldiers are still there helping them.
Moscow says any Russian soldiers fighting in Ukraine are freelance "volunteers", although Ukraine and Western governments said Russia had earlier sent in regular army units.
Source: BBC News Europe