Washington withdrew its ambassador to Damascus after Syrian authorities were implicated in the February 2005 assassination of Rafiq al-Hariri, the former Lebanese prime minister, in Beirut.
Sauerbrey had been expected to meet Meqdad together with a representative of the UN High Commissioner for Refugees (UNHCR), allowing US officials to play down any appearance of bilateral discussions.
The UNHCR official could not attend the meeting, turning it into bilateral talks with Syria, Casey said.
"We said that all concerns in Arab region are linked and it is necessary to engage in a global dialogue on all of them"
Faisal Meqdad, Syria's deputy foreign minister
A State Department official who asked to remain anonymous said the UNHCR official had "some scheduling issues" that allowed Sauerbrey and Meqdad to hold direct talks for 45 minutes.
But in Damascus, the UNHCR said its representative, George Okoth-Obbo, was on a humanitarian aid mission that was separate from Sauerbrey's visit.
Casey said the US and Syrian diplomats spoke exclusively about the plight of Iraq refugees.
"She did call on the Syrian side to work with the Iraqi government, as well as with the UN high commissioner for refugees, to provide protection and assistance for refugees from Iraq that are in Syria," he said.
The Syrians "expressed their willingness to continue hosting displaced Iraqis, although noting the burden that this does place on them and on their system", Casey added.
Afterwards, Meqdad said he expressed to Sauerbrey his wish to schedule bilateral talks with the US on all Middle East issues.
"We said that all concerns in Arab region are linked and it is necessary to engage in a global dialogue on all of them," he told reporters.
"It is impossible to find lasting solutions [to these problems] without such a dialogue."
Sauerbrey is the most senior US official to visit the Syrian capital since Richard Armitage, the then deputy secretary of state, in February 2005.