KIEV, Ukraine — Indiscriminate rocket fire slammed into a market, schools, homes and shops Saturday in Ukraine’s southeastern city of Mariupol, killing at least 30 people, authorities said. The Ukrainian president called the blitz a terrorist attack and NATO and the U.S. demanded that Russia stop supporting the rebels.

Ukrainian officials rushed to defend the strategically important port on the Sea of Azov, beefing up military positions with more equipment and sending in more forces.

The separatists’ top leader declared that an offensive against Mariupol had begun — then later toned down his threats as the scale of the civilian casualties became clear.

President Petro Poroshenko held an emergency meeting of his military officials and cut short a trip to Saudi Arabia to coordinate the government’s response.

“The time has come to name their sponsors. The help given to militants, weapons deliveries, equipment and the training of manpower — is this not aiding terrorism?” Poroshenko said.

Russia insists it does not support the rebels, but Western military officials say the sheer number of heavy weapons under rebel control belies that claim.

A reporter saw convoys of pristine heavy weapons in rebel territory earlier this week.

The rocket attacks came a day after the rebels rejected a peace deal and announced they were going on a multi-prong offensive against the government in Kiev to vastly increase their territory. The rebel stance has upended European attempts to mediate an end to the fighting in eastern Ukraine, which the U.N. says has killed nearly 5,100 people since April.

Mariupol, a major city under government control, lies between mainland Russia and the Russia-annexed Crimean Peninsula. Heavy fighting in the region in the fall raised fears that Russian-backed separatist forces would try to capture the city to establish a land link between Russia and Crimea.

Ukraine’s Defense Ministry said three separate strikes from Grad multiple-rocket launchers hit Mariupol and its surrounding areas Saturday.

“The area that came under attack was massive,” Mariupol mayor Yuriy Khotlubei said. “The shelling was carried out by militants. This is very clearly Russian aggression that has caused terrible losses for the residents of the eastern part of our city.”

The Donetsk regional government loyal to Kiev said at least 30 people — including a 15-year old girl and a five-year old boy — died in the attacks. A Ukrainian military checkpoint near the city was also hit and one serviceman was killed, the Defense Ministry said.

The RIA Novosti news agency cited Ukrainian rebel leader Alexander Zakharchenko as saying an offensive had begun on Mariupol. He spoke as he laid a wreath Saturday where at least eight civilians died when a bus stop was shelled Thursday in Donetsk, the largest rebel-held city in eastern Ukraine.

Zakharchenko swiftly backtracked, however. He denied that his forces were responsible for Saturday’s carnage, saying it was caused by Ukrainian error. He also said the Ukrainian defenses positions around Mariupol would be destroyed but the city itself would not be stormed.

But the Organization for Security and Cooperation’s monitoring mission said the attack on Mariupol was caused by Grad and Uragan rockets fired from areas under rebel control.

Rebel forces have positions six miles from Mariupol’s eastern outskirts. On Jan. 13, a bus near an army checkpoint north of Mariupol was hit by a shell, killing 13 people, an attack Ukraine also blamed on the separatists.

Yulia, a Mariupol citizen who asked that her name not be used for fear of retaliation said Saturday that her stricken neighborhood had no power or heat in the middle of winter due to the attacks. Many residents had boarded up their windows, fearing shattered glass from further attacks, she said.

Reinforcements were being drafted into the city and the Mariupol-based Azov Battalion was being equipped with more heavy weapons, Interior Minister Arsen Avakov said. Security services also detained a spotter suspected of giving rebel fighters coordinates to launch rockets, he said.

Prime Minister Arseniy Yatsenyuk had ordered regional leaders Friday to draw up economic blueprints to put the financially struggling country on a war footing. Ukraine began its fourth wave of mobilization this week, building up manpower for its faltering war effort.

Fighting has also been intensifying for the government-held town of Debaltseve, 31 miles east of Donetsk. The main roads into the town are under separatist control and rebels have vowed to surround the Ukrainian forces stationed there.

U.S. Secretary of State John Kerry said the rebels’ new offensive “has been aided and abetted by Russia’s irresponsible and dangerous decision to resupply them in recent weeks with hundreds of new pieces of advanced weaponry.”

“I join my European counterparts in condemning in the strongest terms today’s horrific assault by Russia-backed separatists on civilian neighborhoods in Mariupol,” Kerry said, citing reports of dozens wounded as well.

He urged Russia to close its international border with Ukraine and withdraw all weapons, fighters and financial backing from the separatists or face increased U.S. and international pressure. The European Union and the U.S. have already hit Russia with sanctions for its actions in Ukraine, moves that have hurt the Russian economy.

EU foreign affairs chief Federica Mogherini echoed Kerry’s demands.

NATO Secretary General Jens Stoltenberg also condemned the Mariupol shelling and what he called the increased presence of Russian forces in Ukraine.

“Russian troops in eastern Ukraine are supporting these offensive operations with command-and-control systems, air defense systems with advanced surface-to-air missiles, unmanned aerial systems, advanced multiple rocket launcher systems and electronic warfare systems,” he said.

A peace deal signed in September in the Belarusian capital of Minsk envisaged a cease-fire and a pullout of heavy weapons from a division line in eastern Ukraine, but that was repeatedly violated by both sides. Foreign ministers from Russia, Ukraine, France and Germany agreed Wednesday to revive that division line but the rebels Friday rejected the whole Minsk deal.

Senior envoys from Ukraine, Russia and the OSCE issued a statement Saturday convening an urgent meeting next week to restart the Minsk peace process.