Story highlights Nearly two-thirds of those who died in the Malaysia Airlines crash in Ukraine were Dutch

In Moscow, people have been leaving flowers and toys outside the Dutch Embassy

Many of the messages include the phrase "forgive me," CNN's Diana Magnay says

One Muscovite told her that Russia's connections with rebels meant it was involved

Outside the Dutch Embassy in Moscow, people have left flowers and cuddly toys at a makeshift memorial for the lives lost in a conflict-scarred corner of eastern Ukraine.

Malaysia Airlines Flight 17 fell from the sky in Donetsk on Thursday, killing all aboard. Of the 298 people killed, 193 -- nearly two-thirds -- were Dutch citizens.

The United States accuses Moscow of supporting the pro-Russian rebels that it suspects shot down the aircraft.

Russia denies involvement, with Russian President Vladimir Putin saying Ukraine's military operation against the rebels is to blame for the tragedy. He has called for a "thorough and objective" investigation.

With rebels in control of the crash area, and reports of bodies and wreckage being tampered with, Dutch Prime Minister Mark Rutte told reporters he had a "very intense" conversation with Putin on Saturday.

Rutte said he told Putin "the opportunity expires to show the world that he is serious about helping."

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The tributes at the Dutch Embassy in Moscow include a hand-drawn picture of a plane broken in midair with the caption "children should not die," in a child's handwriting.

Another message reads: "We are afraid, we are ashamed, we are in mourning."

While the official Russian position is that Russia played no role and has no responsibility for the crash, what's striking in many of the notes is the use of the phrase "forgive us."

The messages give a sense that the people who have left them do feel that Russia has an element of responsibility in what is playing out in eastern Ukraine.

One note reads, in English, "Excuse us, please, if you can. Sorry! Russia, Moscow."

Paying his condolences at the embassy, Muscovite Yuri Yemshanov told CNN it was "difficult to recognize that our country could be involved in this accident."

"I think there's lot of proof that we're in closer relations and connections with the separatists in Ukraine. I suppose it's clearly understood that we support them by providing weapons, and so I think it doesn't matter who launched that rocket. Just because we're supporting terrorists, we're involved."

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His wife, Marina, added: "I think there should be investigation, but of course many things are understood now and we probably could know who did this. Now I think it's time to say I'm sorry for these people. This is the first thing."

Another woman, who gave her name as Olga, said that she was sure Russia was not involved in the tragedy and that an investigation would establish who was, but she added: "However, I would also say 'forgive me.' I'm feeling the same."

Arnold van Sinderen, a Dutch citizen living in Moscow, told CNN he believed that the West painted the wrong image of Putin, but that all the same, the Russian leader needed to step up.

"It's time to take responsibilities there and bring peace in this region. He should take his responsibility as well with what is happening with the plane crash; this might accelerate the situation."

Meantime, the tributes outside the embassy pile up.