"All reports regarding Meshaal's departure are untrue," al-Attiyah told a joint press conference held with Venezuelan Foreign Minister Delcy Rodriguez in the Qatari capital.
Some Arab media outlets reported last week that Qatar had asked Meshaal to leave the country – a claim subsequently dismissed by the Palestinian group.
As for Qatar's relations with Egypt, al-Attiyah asserted that there was no "conflict" between the two countries.
"There are only differences and different points of view, and we are trying to bridge these differences," al-Attiyah said.
Relations between Egypt and Qatar now appear to be on the mend almost a year and a half after they had deteriorated following the ouster of elected President Mohamed Morsi – who Qatar had supported – by the Egyptian military.
Egypt had accused Doha of interfering in its affairs by supporting the ousted leader's Muslim Brotherhood group and hosting a number of wanted Brotherhood figures following Morsi's overthrow.
Cairo has also been incensed by Qatari-owned Al Jazeera's coverage of developments in Egypt and what it describes as biased news coverage against Egypt's current military-backed authorities.
Egypt-Qatar relations, however, began to improve in recent months following mediation efforts by Arab Gulf countries.