Abdullah said Sunday he would not renew two of the treaty's annexes, that allowed Israel to lease two border areas from the Jordanians.
According to Safadi, these rights were due to remain in force for 25 years and will be renewed automatically for the same period unless either country wishes to terminate the arrangement, in which case consultations will be held.
"Baqoura and Ghumar have always been our top priority & our decision is to terminate the Baqoura and Ghumar annexes from the peace treaty out of our keenness to take all decisions that would serve Jordan and Jordanians", Abdullah tweeted. "These circumstances indicate that it is in Jordan's own interest to continue adhering to the peace treaty", he said.
Political analyst Adel Mahmoud said Jordan could face "pressure" from the United States, a key backer of both parties, to push for new negotiations if the Israeli response was negative but that "the king's decision has full popular support".
There was no immediate Israeli reaction.
Despite the two sides sharing close security ties, there has been increased tensions between Jordan and Israel over the Israeli governments "provocative" measures ranging from placing restrictions on the Jerusalem's Al Aqsa Mosque and the Noble Sanctuary - recognised in the peace treaty as under Jordanian custodianship - to the continued construction of settlements on 1967 territory.
Baqura, in the northern Jordan Valley, was captured by Israel in 1950.
Israel's security and intelligence ties with Jordan are more discreet but have likewise strengthened, especially since the Arab Spring uprisings in 2011 and the rise of the Islamic State (ISIS). They have also been expanding economic ties in the a year ago. He dismissed the possibility that Jordan might pull out of other parts of the broader peace treaty. Israel's ongoing occupation of Palestinian territories is also a source of anger among Jordanians.
Activists have been asking the government not to renew the agreement and to annul Israel's ownership of Jordanian lands.
Israel's former ambassador to Jordan, Oded Eran, said he was not surprised by Jordan's decision, and said there was still time for the two countries to re-negotiate the agreement.
More recently, relations have been strained over the status of the flashpoint al-Aqsa Mosque compound, referred to by Jews as the Temple Mount, in Jerusalem and in the aftermath of a shooting at the Israeli Embassy in Amman in which two Jordanian citizens were killed.
In the 1994 peace treaty, Jordanian sovereignty over the area was confirmed but Israelis retained private land ownership and special provisions that allow free Israeli travel. The deal helped Amman to pave the way for U.S. economic and military assistance to the country.