Israeli gunfire killed two Palestinians and wounded at least 35 other protesters along the Gaza border on Monday, health officials said.
Shah's remarks echoed Israeli Prime Minister Benjamin Netanyahu's insistence that Hamas was exclusively culpable for the violence.
He said Israel has an absolute right to engage in "self defense" against the protesters.
The White House on Monday placed sole responsibility on Hamas for the deaths of dozens of Palestinians who've been killed by Israeli forces amid demonstrations against the new USA embassy in Jerusalem.
President Donald Trump had announced the embassy move on 6 December, which immediately sparked violent protests.
The violence made it the deadliest day in Gaza since the devastating cross-border war between the territory's Hamas rulers and Israel four years ago. "Congratulations!" Trump said via Twitter on Monday. "America stands with Israel!"
"Hamas is intentionally and cynically provoking this response", Shah added, suggesting the clashes were "a gruesome and unfortunate propaganda attempt" orchestrated by Hamas' leaders.
The White House says responsibility for dozens of deaths in Gaza coinciding with the opening of the new U.S. Embassy in contested Jerusalem "rests squarely with Hamas".