The Yediot Aharonot, a top-selling daily in Israel, said Netanyahu's actions had irked the United States.
Its report referred to a lawsuit filed in a New York court in 2008 by families of victims of "terrorist attacks" that rocked Israel between May 2004 and January 2007.
They claim the Islamist Palestinian groups Hamas and Islamic Jihad transferred through the Bank of China millions of dollars which were allegedly used to fund the deadly attacks.
Lawyer Nitsana Darshan-Leitner, who represents 22 Israeli families, some of whom have lost relatives in the attacks, slammed Netanyahu for yielding to pressure from China.
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"Netanyahu, who wants to show that he is at the forefront of the fight against terrorism, has given in to considerable pressure from China," she told AFP.
Netanyahu's office has refused to comment the claims, while a senior government official sought to defend the premier.
"But he also knows how to defend the interests of the State of Israel," Steinitz added without elaborating.
But Netanyahu's actions may have harmed ties with top ally the United States by effectively refusing to cooperate with the American judiciary, Yediot reported.
It said Israel's ambassador to Washington, Michael Oren, had travelled to Jerusalem in recent days and met Netanyahu to "inform him that the US adminstration is very upset".
The Bank of China has denied these allegations and said it respect UN regulations concerning money laundering and funding terrorism, the newspaper said.