Abbas made the remarks while meeting members of the Palestinian leadership in the West Bank city of Ramallah. He signed one of the treaties during his televised speech, Xinhua reported.
The decision came after the US failed to convince Israel to release the remaining 26 Palestinian prisoners held in Israeli prisons.
By signing the international treaties, specially the fourth Geneva Conventions, the Palestinians can file complaints and lawsuits against for Israel's human rights violations and settlement activities.
"If Israel is not going to free the remaining group of prisoners, we will sign and join the whole 63 international treaties and organisations," Abbas said.
After upgrading their UN status to a non-member observer state in 2012, the Palestinians become eligible to sign 63 international treaties, conventions and protocols and become members of international institutions such as the International Criminal Court.
Meanwhile, Abbas noted that he does not seek a confrontation with the US, as the latter has been mediating peace negotiations between the Palestinians and the Israel.
When the peace negotiations between the Palestinians and Israel resumed last July, Israel agreed to release 104 Palestinian long-time prisoners in four stages in exchange for halting Palestinians' drive to join international organisations.
However, Israel refused to release the final group of prisoners scheduled to be freed on Saturday unless the Palestinians agree to extend the ongoing peace talks which have been set to end later this month.