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At least 13 people were killed in clashes between Ukrainian troops and pro-Russian rebels which raged in five areas around the wider region.
International monitors said they had abandoned plans to visit the crash site due to fears it was not safe, even though Malaysia said earlier rebels had agreed to provide access.
Ukraine said it was trying to dislodge the rebels, but denied it was fighting near the crash site, saying the separatists had put the monitors off by falsely claiming that the army was operating nearby.
Russia dismissed U.S. allegations it was about to hand over more missiles to the separatists, who Western leaders say almost certainly shot the airliner down by mistake with a Russian-supplied surface-to-air missile.
The separatists deny any involvement and Moscow says it has not supplied them, suggesting Ukrainian forces were to blame.
"Kiev is trying to destroy the evidence of a crime by its army," separatist leader Aleksander Borodai said, referring to a Ukrainian army offensive some distance from the site on Sunday.
With European states trying to minimise the impact of any future sanctions against Russia on their own economies, the U.S. State Department sought to bolster the case for robust action by releasing images it said showed Russian forces had fired across the border at Ukrainian military in the last week.
The images, which show marks on the ground at what the State Department said were launch sites and impact craters around Ukrainian military locations, indicated fire from multiple rocket launchers, the department said.
It also said the images offered evidence that Russia-backed separatists inside Ukraine had fired on Ukrainian forces using heavy artillery supplied by Russia.
Washington said on Friday another transfer from Russia to Ukrainian separatists, this time of heavy-caliber multiple-launch rocket systems, appeared to be imminent and that Russian forces were slowly building up along the Ukrainian border.
Russia said recent international inspections had revealed no evidence of Russian military violations, without giving details.
Members of the European Union, spurred into action by the deaths of 298 people in the airliner, were expected to try to reach a final deal on Tuesday on measures including closing the bloc's capital markets to Russian state banks, an embargo on arms sales and restrictions on dual-use and energy technologies.
The EU added new names on Friday to its list of individuals and companies facing travel bans and asset freezes over their alleged involvement in Ukraine and could agree to extend the list further as early as Monday.
Washington, which has taken the lead in imposing individual and corporate penalties on Russia, said on Friday it was likely to follow up on any new EU move with more sanctions of its own.
The Ukrainian government said its forces were advancing towards the crash site to try to free it from the rebels, who have impeded the work of international monitors and whom Kiev accuses of tampering with evidence pointing to who shot it down.
Only a few international experts have so far been able to get to the site, access to which is negotiated with the rebels.
"All our troops are aiming to get there and liberate this territory so that we can guarantee that international experts can carry out a 100-percent investigation of the site and get all proof needed to deduce the real reason for this tragedy," said Andriy Lysenko, a spokesman for Ukraine's Security Council.
International monitors said the fighting itself could affect the crash site, underlining the growing complexity of trying to establish who shot down Malaysia Airlines flight MH17.
In Donetsk, Alexander Hug, deputy head for the Organization for Security and Cooperation in Europe's monitoring mission in Ukraine, said monitors would not visit the site on Sunday.
"The situation on the ground appears to be unsafe ... we therefore decided to deploy tomorrow morning," Hug, flanked by Dutch and Australian experts, told reporters. "Fighting in the area will most likely affect (the) crash site," Hug said.
An OSCE spokesman said the group would try again on Monday.
The separatists are still in control of the area where the plane was shot down earlier this month but fighting in the wider eastern regions of Donetsk and Luhansk has been heavy as Ukrainian government forces try to drive them out.
It was raging in at least five places on Sunday and Donetsk region health officials said 13 people were killed in fighting in the town of Horlivka, known as Gorlovka in Russian.
Lysenko said troops were advancing east from the town of Makievka towards Shakhtarsk, around 25 km (16 miles) from the crash site. Shakhtarsk residents said air strikes hit the town.
"Our military is advancing, fighting goes on every day, every night, they have already liberated two-thirds of the territory," Lysenko told a news conference in Kiev.
But Ukrainian Foreign Minister Pvalo Klimkin said the Ukrainian army was respecting a no-fight zone within 20 kilometres from the site.
The Russian foreign ministry said Foreign Minister Sergei Lavrov and U.S. Secretary of State John Kerry had agreed on the need to ensure a swift ceasefire in what it described as an "internal conflict".
Earlier, Malaysian Prime Minister Najib Razak said an agreement reached with separatist leader Borodai would "provide protection for international crash investigators" to recover human remains and ascertain the cause of the crash.
The OSCE has provided a team to monitor the site in advance of an investigation, but Najib said a full team of investigators was needed to ensure any human remains left there were removed.
"We also need a full deployment of investigators to have unfettered access to the crash site so we can understand precisely what happened to MH17. I hope that this agreement with Mr Borodai will ensure security on the ground, so the international investigators can conduct their work," he said.
"Three grieving nations", Malaysia, Australia and the Netherlands, had formed a police group to secure the site, he said in a statement issued by his office. The Netherlands and Australia said the mission would not be armed.
Among the 298 people who died aboard the Boeing 777 on its flight from Amsterdam to Kuala Lumpur on July 17 were 193 Dutch nationals, 43 Malaysians and 28 Australians.
Malaysian experts have said they believe at least 30 investigators will be required to cover the full site of the crash, in addition to Dutch investigators and an expert from the United Nations' civil aviation body, the ICAO.
In the Australian capital Canberra, Prime Minister Tony Abbott said an unarmed police mission led by the Netherlands and made up of about 49 officers would travel to the site. Officials said a total of 170 Australian police were deployed in Ukraine.
Abbott, who has played a leading role in pressing for an investigation, told reporters the force would probably stay no longer than three weeks. "Our objective is to get in, to get cracking and to get out," he said.