The statement was posted in response to the over 50 Palestinian rioters shot by Israeli troops after they got too close to the border fence, marking the deadliest day in Gaza in four years.
And in an afternoon press briefing, the White House blamed the fatalities on the enclave's Islamist rulers Hamas.
"What I'm saying is that we believe that Hamas as an organization is engaged in cynical action that's leading to these deaths", Shah answered.
Alistair Burt, Britain's minister for the Middle East, said it was "deplorable that extremist elements may have been seeking to exploit these protests for their own violent purposes".
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The White House said the Jewish state had the right to defend itself.
"The responsibility for these tragic deaths rests squarely with Hamas", Shah said, noting that the administration was aware of the "reports of continued violence in Gaza".
Israeli Prime Minister Benjamin Netanyahu said on Monday that the opening of the US embassy in Jerusalem will be remembered in Israel for generations.
Israel, for its part, has said the demonstrations are orchestrated by Hamas and has insisted its forces are acting "according to standard operating procedures".