The meeting came after the Jordanian monarch was hosted by King Charles III in Buckingham Palace on Thursday.
The talks in No 10 Downing Street also focused on regional and international development projects and ways to improve security and stability around both nations.
King Abdullah stressed to Mr Sunak that collective efforts and solidarity among countries are vital to address the ramifications of Russia’s invasion of Ukraine, particularly on food and energy security.
Counter-terrorism defences was another topic on the agenda, with Mr Sunak and his royal guest discussing both regional and international work on this.
The prime minister “noted the deep-rooted ties between the two countries and keenness to strengthen them further, commending Jordan’s key role in the region”, the royal court in Amman said.
“The prime minister stressed the importance of maintaining bilateral co-operation towards economic prosperity, describing Jordan as one of the United Kingdom’s most important allies in the region.”
He brought his religious and cultural adviser along for the talks, Jordan’s royal court said. It added that peace between Israel and the Palestinian territories was also touched on.
“Concerning the Palestinian cause, the king reaffirmed the importance of working actively to achieve just and comprehensive peace between the Palestinians and the Israelis on the basis of the two-state solution, guaranteeing the establishment of an independent Palestinian state on the 4 June 1967 lines, with East Jerusalem as its capital,” Jordan’s royal court said.
“His Majesty stressed the importance of preserving the historical and legal status quo in the holy city and preventing unilateral Israeli measures that lead to continued escalations in the Palestinian Territories.
“The king added that Jordan will continue to safeguard Islamic and Christian holy sites in Jerusalem under the Hashemite custodianship.”
An agreement signed by the king and Palestinian President Mahmoud Abbas reaffirmed the royal’s custodianship over religious sites in Jerusalem including Al Aqsa Mosque compound.
Continued support for the more than 670,000 refugees Jordan is hosting was also on the agenda in the meeting.
After the Syrian civil war broke out in 2011, Jordan and other neighbouring counties absorbed huge influxes of Syrians fleeing the violence. More than a decade on, many remain in camps run by the UN.
Jordan’s Deputy Prime Minister and Foreign Minister Ayman Safadi and Jordan’s ambassador to the UK Manar Dabbas were present at the meeting, along with several British officials.
A representative for Downing Street said Mr Sunak was please to meet the king a month into his premiership, “given the importance and historic significance of the UK-Jordan relationship”.
“They discussed regional security, including developments in Iraq and Syria and challenges posed by climate change and energy security,” the representative said.
“Both leaders reiterated their shared commitment to peace and stability in the Middle East.
“The prime minister and King Abdullah also welcomed opportunities to deepen co-operation on trade and investment, including new solar and wind power projects and sustainable infrastructure development.”