The State Emergency Service said the search in a remote area of eastern Ukraine roughly 40 kilometers (25 miles) from the Russian border, was being "complicated by armed separatists at the site who hinder the work of SES units."
It said that 380 official staff are taking part in the search for the remains of the 298 people who were on board MH17, covering an area stretching across 34 square kilometers (13 square miles).
They were being helped by busloads of volunteers from local coal mines who fanned out across the wheat fields where the bodies and debris from the plane fell to earth on Thursday.
The situation at the crash site showed some small signs of improvement, with more control and more activity.
But it still remained disorganized in many respects, and the area was still under the control of pro-Russian rebels.
Many of the bodies that had littered the fields previously were gone by late morning Sunday as CNN teams drove through the crash site, but it was not immediately clear where they had been taken.
Government emergency workers prevented vehicles from driving up the road to the main crash site.
But people could still roam around the fields on foot.
The whereabouts of the plane's flight recorders is still unknown.
Rebels control area
Michael Bociurkiw, a spokesman for observers from of the Organization for Security and Co-operation in Europe, said that the group saw men moving an unknown number of body bags on Saturday, but that it wasn't clear who they were.
It's hard to get reliable information because several groups of pro-Russian rebels, some of them masked, control the checkpoints leading to the crash site.
"There doesn't seem to be one commander in charge," Bociurkiw told CNN.
Rebels are suspected of shooting down the plane with a Russian-made surface-to-air missile on Thursday.
Three air crash investigators from Ukraine accompanied the OSCE observers but didn't have much time to do their work, Bociurkiw said.
"They need a lot more time and a lot more freedom of access," Bociurkiw said.
Pressure on Putin Governments from around the world have expressed outrage at the disorderly situation at the crash site and called on Russian President Vladimir Putin to use his influence on the pro-Russian rebels.
"There are multiple reports of bodies being removed, parts of the plane and other debris being hauled away, and potential evidence tampered with," the U.S. State Department said in a statement.
"This is unacceptable and an affront to all those who lost loved ones and to the dignity the victims deserve."
British Prime Minister David Cameron wrote a Sunday Times opinion article urging Putin to find a way to make the crash site more accessible and calm the strife between Ukraine and the rebels.
"If President Putin does not change his approach to Ukraine, then Europe and the West must fundamentally change our approach to Russia," Cameron wrote.
Ten of the passengers on MH17, which was en route from Amsterdam to Kuala Lumpur, were British.
Australian Prime Minister Tony Abbott, whose country had 27 citizens on the plane, added to the pressure on Putin.
Describing the downing of the passenger jet as "a horrific crime," Abbott said he had summoned Russian Trade Minister Denis Manturov, who is visiting Australia, and "made crystal clear my concerns and dissatisfaction with the way this has been handled."
"Russian controlled territory, Russian-backed rebels, quite likely a Russian supplied weapon," Abbott said in a television interview Sunday.
"Russia can't wash its hands of this."
German Chancellor Angela Merkel and Dutch Prime Minister Mark Rutte have spoken out, as well.
"I want to see results in the form of unhindered access and a speedy recovery of the victims' remains," Rutte said Saturday.
Nearly two-thirds of the people on the jetliner were Dutch.
Rutte told reporters he had "an extremely intensive telephone conversation" with Putin on Saturday in which he told the Russian leader that "the window of opportunity to show the world that he intends to help is closing rapidly."
Meanwhile, U.S. Secretary of State John Kerry spoke with his Russian counterpart, Foreign Minister Sergey Lavrov, to urge Moscow to get the rebels to stop fighting and talk peace, and also provide full access to the crash site.
The United States has said evidence suggests a Russian-made surface-to-air missile fired from the rebel territory took down the Malaysia Airlines Boeing 777 with citizens from more than 10 nations aboard.
U.S. President Barack Obama said Friday that Russia likely bears some of the responsibility, noting rebel fighters couldn't have operated the missile "without sophisticated equipment and sophisticated training, and that is coming from Russia."
U.S. officials believe the missile systems may have been moved back across the border into Russia, CNN foreign affairs reporter Elise Labott said Saturday.
Russia has denied any involvement, and Putin said Ukraine's military campaign against the rebels was to blame.
He also has called for a "thorough and objective investigation" of the crash.
Since the crash, the Ukrainian government and pro-Russian rebels have traded bitter accusations over who was responsible and what has been done since.
Ukrainian officials have said that a Russian-made Buk M1 missile system, brought into eastern Ukraine from Russia, had shot down the Malaysian airline.
The Ukrainian government has accused the rebels of removing debris and 38 bodies from the scene as part of an attempt to cover up what happened.
The local head of the rebels, Alexander Borodai, has rejected accusations that his forces shot down the plane, telling reporters that the rebels lacked the firepower to hit an aircraft so high up.
Borodai, who calls himself the prime minister of the self-styled Donetsk People's Republic, also denied that his forces removed any bodies.
Where are the black boxes?
One key issue for investigators is the location of the plane's flight data recorders, which may hold crucial data.
The Ukrainian government said Friday that the so-called black boxes are still in Ukrainian territory but didn't clarify whether they were in Ukraine's possession.
Bociurkiw of the OSCE said no one at the crash site was able to tell his people where the recorders might be.
Malaysian investigators touched down in Kiev on Saturday to try to get the bottom of what happened to the jetliner.
But Malaysia's official news agency Bernama said they were still negotiating with pro-Russian rebels over access for their 131-member team.
Malaysian Transport Minister Liow Tiong Lai said Saturday in Kuala Lumpur that Malaysia was "deeply concerned that the crash site has not yet been properly secured."
"There are indications that vital evidence has not been preserved in place," he said.
Law enforcement officials from the Netherlands, the United States and Australia have arrived or are being sent to Ukraine to work with the investigation, which is being led by the Ukrainian government in Kiev.
Malaysia Airlines said Sunday that it will retire the flight number MH17 for the route from Amsterdam to Kuala Lumpur, replacing it with the code MH19.
The change, which will take effect Friday, is being made "out of respect for the crew and passengers," the airline said.
Nationalities aboard MH17
- 193 Dutch (including 1 dual Netherlands/U.S. citizen)
- 44 Malaysian (including 15 crew, 2 infants)
- 27 Australian
- 12 Indonesian (including 1 infant)
- 10 British (including 1 dual UK/South African citizen)
- 4 German
- 4 Belgian
- 3 Filipino
- 1 Canadian
- 1 New Zealander
Source: CNN World