The Journal cited U.S. officials as saying they now suspect that Russia supplied the rebels with multiple SA-11 systems by smuggling them in with other equipment, including tanks.
Fighting flared in eastern Ukraine on Saturday. The government said it was pressing its offensive in the east.
Observers from Europe's OSCE security agency visited part of the crash site near the village of Hrabove for a second day on Saturday and again found their access hampered by armed men from the forces of the self-declared People's Republic of Donetsk. An OSCE official said, however, they saw more than on Friday.
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At one point, a Reuters correspondent heard a senior rebel tell the OSCE delegation they could not approach the wreckage and would simply be informed in due course of an investigation conducted by the separatists. However, fighters later let them visit an area where one of the airliner's two engines lay.
"The terrorists, with the help of Russia, are trying to destroy evidence of international crimes," the Ukrainian government said in a statement. "The terrorists have taken 38 bodies to the morgue in Donetsk," it said, accusing people with "strong Russian accents" of threatening to conduct autopsies.
Ukraine's prime minister said armed men had barred government experts from collecting evidence.
Kerry told Lavrov the United States was "very concerned" over reports that the remains of victims and debris had been removed or tampered with, the State Department said. He said Washington was also concerned over denial of "proper access" for international investigators and OSCE monitors.
"This is unacceptable and an affront to all those who lost loved ones and to the dignity the victims deserve," Kerry's spokeswoman, Jen Psaki, said in a statement. "We urge Russia to honor its commitments and to publicly call on the separatists to do the same."
Ukrainian President Petro Poroshenko urged the United Nations to label rebels fighting his forces in the eastern regions of Luhansk and Donetsk as belonging to "terrorist organizations".
In the regional capital Donetsk, the prime minister of the separatist authorities told a news conference that Kiev was holding up the arrival of international experts whose mission to investigate the cause - and potentially blame - for the disaster was authorized on Friday by the U.N. Security Council.
Contrary to earlier statements by the rebels, Alexander Borodai said they had not found the black box flight recorders. He said rebels were avoiding disturbing the area.
"There's a grandmother. A body landed right in her bed. She says 'please take this body away'. But we cannot tamper with the site," Borodai said. "Bodies of innocent people are lying out in the heat. We reserve the right, if the delay continues ... to begin the process of taking away the bodies. We ask the Russian Federation to help us with this problem and send their experts."
At Hrabove, one armed man from the separatist forces told Reuters that bodies had already been taken away in trucks. Another said people had looted valuables immediately after the crash. But fighters and local people say they have been doing their best to collect evidence and preserve human remains.
As the stench of death began to pervade the area after Thursday's crash, correspondents watched rescue workers carry bodies across the fields and gather remains in black sacks.
The Ukrainian security council in Kiev said staff of the Emergencies Ministry had found 186 bodies and had checked some 18 sq km (seven square miles) of the scattered 25-sq-km (10-square-mile) crash site. But the workers were not free to conduct a normal investigation.
"The fighters have let the Emergencies Ministry workers in there but they are not allowing them to take anything from the area," security council spokesman Andriy Lysenko said. "The fighters are taking away all that has been found."
Ukraine accuses pro-Russian rebels of destroying evidence
Malaysia, whose national airline has been battered by its second major disaster this year, said it was "inhumane" to bar access to the site around the village of Hrabove, but said Russia was doing its "level best" to help.
A team of Malaysian experts flew in to Kiev on Saturday and experts from Interpol are due there on Sunday to help with the identification of victims. Dutch, U.S. and other specialists are being lined up to help in the investigation.
"Any actions that prevent us from learning the truth about what happened to MH17 cannot be tolerated," Malaysian Transport Minister Liow Tiong Lai said on Saturday before leaving for Kiev. "Failure to stop such interference would be a betrayal of the lives that were lost."
The deadliest attack on a commercial airliner follows the disappearance of Malaysia Airlines' Flight MH370 in March with 239 passengers and crew.
The scale of the disaster could prove a turning point for international pressure to resolve the crisis in Ukraine, which has killed hundreds since pro-Western protests toppled the Moscow-backed president in Kiev in February and Russia annexed the Crimea peninsula a month later.