Mariupol , Ukraine ( CNN ) -- Shelling hit areas near two key cities in eastern Ukraine on Sunday , intensifying fears that a ceasefire that took effect less than two days ago may be falling apart . The fledgling truce between the Ukrainian government and pro-Russian rebels began Friday evening , and both sides were already accusing each other of violating it by Saturday . Sporadic artillery and machine gun fire rang out in the early hours of Sunday on the outskirts the strategic port city of Mariupol . A gas station was set on fire , and cars carried wounded civilians down the roads . Shelling and explosions were also heard near the airport of the flashpoint city of Donetsk on Sunday morning , the city council said on its website . In both cities , the source of the weapons fire was n't immediately clear . The Mariupol city government said that pro-Russian rebels had carried out the shelling near the city overnight . It said one woman was killed and three people wounded . The Russian state news agency ITAR-Tass late Saturday quoted rebel officials as saying that Ukrainian forces continued to shell Donetsk and rebel positions near Mariupol . The RIA Novosti news agency reported that four Donetsk residents were killed in the shelling . Ukrainian National Security and Defense Council spokesman Col. Andriy Lysenko told reporters in Kiev on Saturday that the situation was calmer than before the truce , but that there had been a number of `` provocations '' by rebels . They included 10 instances of shelling in the Donetsk and Luhansk regions , he said . In a sign the government was still hoping to stick to the ceasefire deal , Lysenko said a prisoner exchange would begin soon , although he did n't specify a time or date . Does ceasefire in Ukraine have any chance of holding ? 'So much confusion ' Ukrainian forces and pro-Russian rebels have been locked in vicious fighting in eastern Ukraine since April , leaving more than 2,200 people dead , according to the United Nations . The conflict has triggered a humanitarian crisis in the region , where shelling has destroyed homes and infrastructure . Nationwide , more than a million people have been displaced from their homes by the fighting , most of them in the East . One old man in Mariupol shook his head gloomily when asked if he thought the ceasefire would last . `` There is so much confusion , '' Gennady Andreyavich said . `` We really do n't know what will happen , because when people say we must live in a united Ukraine and we see at the same time Ukrainian forces in retreat -- what should we think ? '' Ukrainian forces and the rebels have engaged in fierce fighting over the past week in the territory between the Russian border and Mariupol . A previous unilateral ceasefire declared by the Ukrainian government in June broke down after 10 days . Poroshenko and Putin talk . Ukrainian President Petro Poroshenko had a phone conversation with Russian President Vladimir Putin after the signing of the ceasefire deal in the Belarusian city of Minsk , Poroshenko 's office said Saturday in a statement . The leaders agreed that the ceasefire in eastern Ukraine has been mostly upheld and they discussed further steps to make the truce last , the statement said . Some areas at the heart of the conflict reported that calm was prevailing . Luhansk city council said that Saturday was the first day in over a month with no shooting . The city office has started working on repairs to the power and water supply . Russian warning over sanctions . In spite of the ceasefire agreement , Putin remains under pressure from the West over Russia 's actions in Ukraine . The Ukrainian government and the West accuse Moscow of supporting the rebels with weapons and fighters -- allegations that Moscow has repeatedly denied . Hours after the truce went into effect , EU leaders meeting in Brussels , Belgium , agreed on a new round of economic sanctions against Russian interests . They are due to be formally adopted on Monday . Earlier last week , Poroshenko hinted at other ways that the West might aid Ukraine . At a news conference during the NATO summit on Thursday , Poroshenko said Western powers assured him that the possibility of lethal aid was on the table , in addition to nonlethal aid . `` As a result of our bilateral consultations , almost every country stated its assistance to Ukraine , '' Poroshenko said . `` First and foremost , this concerns military and technical cooperation , both nonlethal and lethal weapons , including precision guidance weapons . '' The United States , France and other NATO allies have not independently confirmed whether lethal aid is an option . Russia 's Foreign Ministry warned Saturday that if new EU sanctions are imposed , Russia `` certainly will respond , '' ITAR-Tass reported . Amnesty International , meanwhile , accused Ukrainian militias and rebels of carrying out war crimes . The human rights group singled out Russia for a buildup of armor and artillery in eastern Ukraine . Putin has voiced sympathy for the rebels , many of whom are ethnic Russians . But he denies that Russia has armed and trained the rebels , or sent its troops over the border . NATO : An amusing show for Putin ? NATO 's moment of truth on Ukraine . CNN 's Diana Magnay reported from Mariupol , and Jethro Mullen wrote and reported from Hong Kong . CNN 's Laura Smith-Spark , Lindsay Isaac , Reza Sayah , Michael Martinez and Alla Eshchenko contributed to this report . Journalist Victoria Butenko also contributed from Kiev .
A woman is killed in shelling near Kiev , the local resident says . Shelling and explosions heard near Donetsk airport , city official says . Kiev and pro - Russian rebels have blamed each other for security problems . ` ` There is so much confusion , '' a local resident says .