Another 102 people were injured, at least 75 of whom needed hospital treatment, and many suffered shrapnel injuries, Mariupol City Council said.
Pro-Russian separatists are blamed for the attack on residential areas in the port city, Donetsk regional police chief Vyacheslav Abroskin said on his Facebook page.
The Interior Ministry said one person was arrested in connection with the attack.
Based on preliminary assessments, the shells were fired from Grad rocket systems, a statement from Mariupol City Council said.
The statement also said the situation was under control, and urged residents not to panic but to rely on information from official sources only.
Monitors with the Organization for Security and Co-operation in Europe
said they conducted a crater analysis which showed the use of Grad and Uragan rockets that likely originated from areas controlled by the pro-Russian rebel group Donetsk People's Republic (DPR).
The shelling comes amid a surge in fighting between government forces and pro-Russian separatists.
U.S. Secretary of State John Kerry warned of increased international pressure on Russia.
"We call on Russia to end its support for separatists immediately, close the international border with Ukraine, and withdraw all weapons, fighters and financial backing," Kerry said in a statement.
The White House says Vice President Biden spoke with Ukraine President Poroshenko on Saturday.
They "expressed grave concern over Russia's blatant disregard for its commitments under the September Minsk agreement and unilateral escalation of the conflict," the White House said.
The two leaders vowed to "ensure that the costs continue to rise on Russia for its aggressive actions against Ukraine."
Thousands have been killed since the conflict broke out in the spring of last year and a ceasefire agreed to in September in Minsk, Belarus, crumbled long ago.
'Callous disregard for human life'
U.S. officials took to Twitter to condemn the latest violence.
"Today's indiscriminate shelling of Mariupol (is) part of an apparently Russian-backed general offensive in complete violation of Minsk agreements," said U.S. Ambassador to Ukraine Geoffrey Pyatt.
"Russia's escalation continues -- Kremlin's callous disregard for human life (incl Russian soldiers) on full display in Ukraine," said Daniel Baer, the U.S. ambassador to the Organization for Security and Cooperation in Europe (OSCE).
The foreign ministers of Ukraine and Russia met this week in Berlin to discuss a way out of the violence. But despite the talks, violence in the breakaway Donetsk and Luhansk regions shows no sign of abating.
Thursday's shelling of a transit stop
in Donetsk city -- an attack that Ukraine's Defense Ministry blamed on rebels -- killed eight civilians, according to state news reports. But Ukrainian troops have come under heavy fire as well.
That includes 115 attacks in a recent 24-hour period that killed three troops and wounded 50 more, Ukrinform, the Ukrainian national news agency, reported Friday.
The OSCE monitoring mission in Ukraine condemned continuing fighting in civilian areas in a statement Saturday and urged both sides to refrain from using force in such areas, including near Donetsk airport.
"Using residential areas as firing positions attracts counter-firing to these areas, further endangering the lives of civilians," it said.
"All parties need to take robust and immediate action in order to end the new escalation in fighting and its heavy toll on civilians."
Moscow denies accusations
Ukraine and the West accuse Russia of sending troops and equipment over the border. In a bid to put pressure on Moscow over Ukraine, the United States and European Union have imposed financial sanctions against Russian interests.
Wednesday, for instance, Ukrainian President Petro Poroshenko said "more than 9,000 Russian troops (crossed) our Russian-Ukrainian border, bring with them hundreds and hundreds of tanks, armed personnel carriers, and killing Ukrainian civilians and attacking Ukrainian troops."
Moscow denies the claims.
Russian President Vladimir Putin blamed the wave of recent casualties on those giving the order to fire in heavily populated areas, in remarks reported by the state-run Itar-Tass news agency Friday.
"Those who give such criminal orders bear responsibility for this. People doing that should know that there is no other way of resolving such conflicts than peace negotiations and political measures," he said.
Putin also suggested Ukraine was not interested in finding a peaceful resolution to the crisis and said he hoped "common sense" would prevail.
The conflict in eastern Ukraine broke out after Russia annexed Ukraine's southeastern Crimea region, as pro-Russia separatists claimed control of the Luhansk and Donetsk regions.
From mid-April 2014 to January 21, the conflict killed at least 5,086 people and injured at least 10,948 others, according to the United Nations.
"We fear that the real figure may be considerably higher," the Office of the U.N. High Commissioner for Human Rights said about the death toll in a report released Friday.