U.S. President Obama also put the blame on Moscow, warning that the United States would work with European partners to "ratchet up the pressure on Russia."
Separatist leader Alexander Zakharchenko initially announced that his forces had begun an offensive on the government-controlled city of Mariupol.
But after the extent of civilian casualties became known, he backtracked and blamed Ukrainian forces for Saturday's carnage.
The rocket attack came a day after the rebels rejected a peace deal and announced they were going on a multi-pronged offensive against the Kiev government in Kiev in a bid to seize more territory.
The rebel stance has upended European attempts to mediate an end to the fighting in eastern Ukraine that has cost at least 5,100 lives since April, according to United Nations estimates.
In Mariupol on Sunday, emergency workers disposed of rocket fragments at the scene of the attack.
Police said two unexploded rockets were found in a bank and an apartment building.
U.N. refugee agency workers handed out blankets to people left homeless or without heat because of the shelling, which hit schools, homes and shops.
"The city is in shock," Mariupol resident Yelena Khorshenko said by telephone.
"The streets are empty, and people are boarding up their windows and preparing for the worst."
Mariupol lies between Russia and Russian-annexed Crimea.
Heavy fighting in the region in the fall raised fears that the Russian-backed separatists would try to capture the city to forge a land link between the two.
A peace deal signed in September envisaged a cease-fire and a pullout of heavy weapons from a division line in eastern Ukraine, but both sides have repeatedly violated the pact.
The United States was "deeply concerned about the latest break in the cease-fire and the aggression that these separatists with Russian backing, Russian equipment, Russian financing, Russian training and Russian troops are conducting," Obama said during a visit to New Delhi.
"And we will continue to take the approach that we've taken in the past, which is to ratchet up the pressure on Russia and I will look at all additional options that are available to us short of military confrontation and try to address this issue."
Obama said the U.S. would work "in close consultation with our international partners, and particularly European partners, to ensure that they stay in lock-step with us on this issue."