Debris of the Malayasian airline scatter everywhere in Grabovo, Ukraine, Thursday July 17, 2014. Photo: AP
The downing of Malaysia Airlines jet MH17 in eastern Ukraine may constitute a "war crime", the UN human rights chief Navi Pillay says.
Ukraine and Western governments believe pro-Russian rebels shot down MH17, using a Russia-supplied missile system.
Moscow and the rebels have blamed Ukrainian forces for the plane crash.
All 298 people on board - mostly Dutch - died on 17 July. Heavy fighting has again prevented an international police force from reaching the crash site.
The Ukrainian military said it was battling separatists for control of several towns near the site in eastern Ukraine.
The international police want to help secure the huge site so that plane wreckage and human remains can be examined by international crash experts.
Most of the bodies have been removed, many of them repatriated to the Netherlands.
"This violation of international law, given the prevailing circumstances, may amount to a war crime," Pillay, the UN High Commissioner for Human Rights, said of the downing of MH17.
"Every effort will be made to ensure that anyone committing serious violations of international law including war crimes will be brought to justice, no matter who they are," Pillay said.
At least 1,129 people have been killed and 3,442 wounded in the Ukraine conflict since mid-April, the UN said.
The conflict has displaced more than 200,000 people, many of whom have fled east to neighbouring Russia.
Russian Foreign Minister Sergei Lavrov said on Monday he hoped that monitors from the OSCE international security body would be able to deploy on the Ukraine-Russia border in the next few days.
In a statement on Monday, the Ukrainian military said it had "entered" the towns of Shakhtarsk and Torez and was working to seize control of Pervomaysk and Snizhne - all close to the crash site of MH17.
A team of Australian and Dutch police and forensic experts was forced to abandon attempts to reach the site on Monday due to the security situation in the area. It was the second failed attempt in as many days.
The army is also trying to take control of two main roads in eastern Ukraine, which the government in Kiev believes to be vital supply lines from Russia for rebel forces in Donetsk.
In the past 24 hours there has been heavy artillery fire at the city of Horlivka, where several civilians were killed.
In the city of Donetsk at least three people died in shelling too, the municipal authorities say. And there are reports of civilian casualties as a result of the shelling of Luhansk, which is also held by the rebels.
Last week, the US-based Human Rights Watch said both sides in the conflict were using unguided Grad rockets against civilian areas, in violation of human rights norms, and urged them to stop doing so. It documented several attacks in which, it said, the rockets were apparently fired by government forces.
The US has produced what it calls satellite evidence that rockets have been fired at Ukrainian forces from Russian soil.
Russia denies that any of its forces are helping the rebels.