Speaking in the South African capital, Pretoria, today, Abbas said it is important that the Israeli government and citizens consider what the proposed law may mean for peace in the region.
Israeli Prime Minister Benjamin Netanyahu is promoting a bill to have the country's constitution declare it a Jewish state.
Critics of the bill say it discriminates against Israel's Arab minority who make up about a fifth of the population of 8 million.
Abbas is on a three day state visit to South Africa, where he met with President Jacob Zuma to discuss security in the Middle East, including tensions at the al Aqsa mosque in Jerusalem.