In their joint meeting in the French capital, Abbas told Olmert he has never officially opposed to the peace initiative presented to him, as reported by the Palestinian official news Agency Wafa.
"I very happy to meet President Abbas, we haven't met for a long time," Olmert said during the meeting.
"Abbas is the president of the Palestinian people, a great leader and the most interesting figure (to play a role-ed) in the future developments of the Israel-Palestinian relations," the former prime minister added.
After the meeting concluded, Olmert said in a statement to the Palestinian media that "US and Europe, and certainly Israel must understand there is no substitute to the two-state solution and that Abbas is the only person who can realize this solution."
"The PA President has proven in the past he is committed to the two-state solution and for that he earned my respect.
"The Palestinians comprehend (Abbas is committed to the two-state solution) and it is important Israel understands this as well. Abbas is fighting against terror as part of his obligation to achieve peace," Olmert went on to say.
"I consider Abbas as my friend since the time we've worked together. I believe, as he does, that achieving peace is possible.
"Both me and Abbas are confident that had I completed my tenure (as prime minister), peace would have become a reality years ago," he elucidated.
According to Abbas, if Olmert would have remained in power for a few more months, a peace agreement would have been signed between Israel and the Palestinians.
Earlier, Abbas met with French President Emmanuel Macron and told him the Palestinians are willing to negotiate, "as opposed to Israel's claims."
"Israel is the one objecting to holding peace talks. We are prepared for both overt and covert negotiations led by the Middle East Quartet, as well as Western and Arab countries," Abbas elaborated.
He added that he clarified his stances to Macron and that he would also convey them to US President Donald Trump before the United Nations General Assembly in New York next week.
IDF Chief of Staff Gadi Eisenkot warned the Security-Cabinet at the beginning of the week that there is more than a moderate chance that a violent conflagration could erupt in the West Bank, adding that the US decision to choke the Palestinian Authority (PA) of financial funds is counter productive for Israel and could inflame matters in the area.
Eisenkot was raising objections to the numerous measures being taken that he said would only push PA President Mahmoud Abbas into a corner and potentially create an intransigent leader unwilling to cooperate with Israel on security matters.
Among the factors raised was the recent American announcement that the White House would halt funding for the last aiding source beneficial for the Palestinians.
Eisenkot also lamented the failed reconciliation deal between the PA and the Hamas terror group in Gaza and noted that the aging Palestinian leader, beset by poor health, could lose control of the area as unrest remains in Gaza and anger reaches boiling point in the West Bank.
The defense establishment believes that Abbas’s 2015 speech at the UN inspired the wave of terror that ensued, which was marked by daily car-ramming, stabbing and shooting attacks by lone wolf Palestinian terrorists throughout Israel.
With the US pressure mounting on the 82-year-old leader, the defense establishment attaches significance to his upcoming speech, which is expected to be a defiant declaration against US President Donald Trump and a tacit imprimatur for fresh terror attacks.