Mr. Tillerson arrival in Egypt is a regional tour amid heightened tensions between Israel and Syria after an Israeli F-16 aircraft was shot down.
Australian and New Zealand soldiers have trained more than 30,000 Iraqi troops in the fight against Islamic State militants since 2015. An official statement also emphasized Amman's role in helping the USA in the fight against the Islamic State and counter terrorism in general.
Despite Trump's repeated threats to cut assistance to such nations, Secretary of State Rex Tillerson and Jordan's Foreign Minister Ayman al-Safadi signed the increased aid package, which represents a 27-percent increase over current levels and is two years longer than the existing one negotiated by the Obama administration.
"Without continued attention and support from coalition members, we risk the return of extremist groups like ISIS in liberated areas in Iraq and Syria, and their spread in new locations", Tillerson said, referring to the spread of ISIS "franchises" to Afghanistan and the Philippines, among other countries.
Tillerson, speaking at a meeting in Kuwait of the US-led global coalition against Daesh, also said Washington had chose to provide an additional $200 million of aid to stabilize liberated areas in Syria.
His final stop will be Thursday in Turkey, which sees USA support for Kurdish militia in Syria as a grave national security threat.
The Trump administration's Middle East peace plan is "fairly well advanced", Secretary of State Rex Tillerson said Wednesday, as he sought to convince regional allies that the US remains an honest broker despite recognizing Jerusalem as Israel's capital. The operation is carried out against Kurdish SDF-affiliated People's Protection Units (YPG), which Ankara believes have links to the Kurdistan Workers' Party (PKK), designated as a terrorist organization in Turkey.
Tillerson said Washington had to "find a way to continue to work in the same direction".
"Doing business in Iraq can be complicated, but the Iraqi market has vast potential", said Tillerson, saying the country had demonstrated it was "open for business".
"As you know, we made our position on Jerusalem clear and we view these final-status issues as needing to be negotiated among the parties on the basis of a final solution", Mr. Safadi said while sitting beside Mr. Tillerson.
Iraq was shattered following the 2003 US invasion and the resulting occupation and civil war.
Australia last month brought home its six Super Hornet fighter jets after ceasing air strike operations against IS in Iraq and Syria.