The resolution, which had been drafted by Australian diplomats, was adopted unanimously on Monday.
It condemned the apparent shooting down of the Malaysia Airlines passenger jet over rebel-held eastern Ukraine last week. It demanded that those responsible "be held to account and that all states cooperate fully with efforts to establish accountability." It also called on all armed groups in the region to ensure "safe, secure, full and unrestricted access" for international investigators.
The passage of the resolution followed a weekend of intense negotiations and widespread pressure on Russia to support the measure.
Obama addresses Putin
This came just hours after US President Barack Obama used a statement to reporters at the White House to demand that his Russian counterpart, Vladimir Putin, use his considerable influence over separatist rebels in eastern Ukraine to ensure investigators full access to the wreckage of flight MH17.
Obama said it was clear that pro-Russian separatists who control the territory where flight MH17 came down last week were continuing to prevent international investigators from gaining full access to the wreckage.
"President Putin says that he supports a full and fair investigation, and I appreciate those words, but they have to be supported by actions," Obama added.
While he didn't directly raise the possibility of imposing fresh, tougher sanctions on Russia, Obama indicated that these could be in the offing. He said that if the Kremlin continued to back the rebels in eastern Ukraine, "the costs for Russia's behavior will only continue to increase."
Obama was speaking shortly before Malaysian Prime Minister Najib Razak announced in a televised statement that he secured an agreement with the rebels under which the bodies of the victims would be handed over to Dutch officials and that the black boxes would be turned over to a Malaysian team.
Malaysian Airlines flight MH17 crashed last Thursday, killing all 298 people on board. Of these, 193 were Dutch nationals.
pfd/mg (AFP, AP, Reuters, dpa)