Obama met Abbas Tuesday at the United Nations in New York, both men accompanied by retinues that included their nations' top diplomats and U.N. representatives.
After the meeting, Obama said the last time the two met -- in Ramallah during the U.S. president's visit to Israel and the West Bank -- he told both the Israelis and the Palestinians the United States "remains deeply committed to bringing about a just and lasting peace to a conflict that has been going on too long."
"And I want to say that President Abbas, I think, has consistently rejected violence, has recognized the need for peace, and I'm grateful to him for his efforts," Obama told reporters Tuesday.
Obama reiterated the U.S. position that Israeli-Palestinian border "should be based on 1967 lines with mutually agreed-to swaps so that secure and recognized borders are established for both states with robust security provisions so that Israel retains the ability to defend itself, by itself, against any threats."
He said he was "very pleased that President Abbas has been willing to enter into negotiations. Sitting directly at the table, we've seen Palestinian and Israeli representatives discuss some of the most difficult issues that have been roadblocks to peace for too long."
Abbas, speaking through an interpreter, said Palestinians are "fully committed to the peace process so that we can reach a final settlement that ultimately will lead to the creation of an independent Palestinian state that would live side-by-side in peace and security with Israel."
"And as you have indicated, Mr. President, we have no illusions that peace will be easy or simple," Abbas said. "And we have to overcome several difficulties, but we realize that peace in the Middle East is not just important for the Palestinians and Israelis, it's important for the entire region and the world."
The meeting came after Abbas, in a meeting with Jewish leaders in New York, publicly condemned the killings of two Israeli soldiers.
It is the first official Palestinian public condemnation of the deaths of Israeli Sgts. Gal Gabriel Kobi and Tomer Hazan in separate West Bank incidents during the weekend.
Kobi was killed by a suspected Palestinian sniper in Hebron Sunday night and Hazan was allegedly killed by a Palestinian who dumped the body in a well near Qalqilya Friday.
Abbas condemned the killings Monday when answering a question by former U.S. Secretary of State Madeleine Albright at a dinner hosted by the S. Daniel Abraham Center for Middle East Peace, the Times of Israel reported.
Israel Radio said Abbas condemned all instances of violence against citizens, adding he expects Israel to condemn the deaths of four Palestinians by the Israeli army in recent weeks.
Referring to peace talks with Israel, Abbas said he seeks a "just and everlasting comprehensive peace" with Israel, the official Palestinian news agency WAFA reported.
"We have a true opportunity to achieve a lasting, just and comprehensive peace and we can do it without any mistakes. We need your support to guarantee a successful end to peace talks so that the state of Palestine can live in peace and security alongside the state of Israel on the 1967 borders," the news agency quoted Abbas as saying.
He called on Israel to focus on building peace rather than building settlements, saying the current negotiations are the last opportunity for peace.
"This is the time to achieve peace in the Holy Land. This is the right time for Jews, Christians and Muslims to show similarity and greatness of these three religions. It is time to replace hate, conflict, bloodshed and incitement with cooperation," he said.
Abbas said 57 Arab and Muslim nations will normalize ties with Jerusalem if Israel withdraws from Arab land it occupied in 1967.
2014: The Year in Music [PHOTOS]