Iraq, Egypt and Jordan hold tripartite summit in Baghdad
Iraq is also seeking to establish itself as a mediator between Arab countries and Iran, after reportedly hosting talks in April between Tehran and Riyadh.
Sisi and Abdullah met Iraqi President Barham Saleh and Prime Minister Mustafa al-Kadhemi, with Saleh saying the encounter was "an eloquent message amid enormous regional challenges".
"Iraq's recovery paves the way to an integrated system for our region built on the fight against extremism, respect for sovereignty and economic partnership," Saleh said on Twitter.
The summit held between Kadhemi and his guests broached regional issues, as well as ways of bolstering cooperation between Iraq, Jordan and Egypt in the fields of security, energy and trade, according to a joint statement released at the end of the meeting.
The leaders discussed a "political solution" to Syria's 10-year civil war based on UN resolutions "that would preserve its security and stability and provide adequate conditions for the return of refugees".
The Syria conflict has killed hundreds of thousands and displaced millions, with refugees flooding the borders of neighbouring countries including Jordan, which lacks in resources and faces economic hardships.
The leaders welcomed efforts underway to restore stability in Libya and Yemen, and called for the departure of foreign forces and mercenaries from Libya.
They called for renewed efforts to reach a "just and comprehensive peace" between Israel and the Palestinians, and for the creation of an independent Palestinian state.
They also hailed Egypt's role in negotiating an end to deadly hostilities between Israel and the Gaza Strip's Islamist rulers Hamas in May, and Cairo's pledge to help rebuild the coastal enclave.
Kadhemi had set the tone at the start of the summit, saying the three countries would "try to shape a common vision... through cooperation and coordination" regarding Syria, Libya, Yemen and Palestine.
Sisi is the first Egyptian president to visit Baghdad since Iraqi dictator Saddam Hussein's troops invaded Kuwait in 1990.
Relations between Baghdad and Cairo have improved in recent years, and officials from the two countries have conducted visits.
The Jordanian king visited in early 2019 for the first time in 10 years.
Media reports revealed that Iranian and Saudi officials met in Baghdad in April, their first high-level meeting since Riyadh cut diplomatic ties with Tehran in 2016.
Iraqi analyst Ihsan al-Shamari said that Sunday's summit was "a message for the United States that Iraq will not only have relations with Iran at the expense of Arab countries".
In a statement, US State Department spokesman Ned Price said Washington welcomed the "historic" visit, and called it "an important step in strengthening regional economic and security ties between Egypt, Iraq, and Jordan and to advance regional stability".
Analysts have long said that Iraq is a battleground for influence between arch-foes Washington and Tehran with whom it maintains good relations.