But Baird played down expectations that his visit could see Canadian-Egyptian Mohamed Fahmy freed imminently after more than a year in jail.
"We are all working toward seeing a constructive resolution on that sooner rather than later," he said at a press conference with Egyptian Foreign Minister Sameh Shoukry.
"I didn't leave Canada with any expectation that we will solve the issue today, but we had an open constructive dialogue," said Baird, who signed agreements with Egypt on security funding and diplomatic training.
Baird said last week that he was close to reaching a deal with Egypt on deporting Fahmy, who was jailed with Australian Peter Greste and Egyptian Baher Mohamed after a trial that sparked global condemnation.
His office had said before his visit that he would meet Egyptian President Abdel Fattah al-Sisi, but a diplomat said Thursday that there would be no such meeting after all.
Fahmy and his two al-Jazeera colleagues were convicted of aiding the blacklisted Muslim Brotherhood and defaming Egypt, and sentenced to between seven and 10 years in prison. An appeals court this month ordered a retrial but kept them in custody.
The imprisonment of the journalists has embarrassed the Egyptian government, with Washington and the United Nations leading calls for their release.
Sisi, the former army chief who overthrew president Mohamed Morsi in 2013 and then won an election, has said he wished the journalists had been deported from the beginning. He has since enacted a law that allows Egypt to deport foreign nationals standing trial in Egypt, or convicted of crimes, to their home country.
According to Fahmy's brother, a request has been submitted to have him deported from Egypt under the new law. Greste's lawyer has submitted a similar request, while Mohamed's wife has said she also is looking at ways to get her husband out of Egypt.
Egyptian police arrested Fahmy, Greste and Mohamed in December 2013, at the peak of a diplomatic row between Cairo and Qatar, which owns al-Jazeera. The broadcaster had been critical of the deadly crackdown on Morsi's Muslim Brotherhood movement following the leader's overthrow.
Qatar has since moved to mend ties with Egypt and al-Jazeera shut down its Arabic-language Egyptian affiliate channel, which supported the Muslim Brotherhood.
The rapprochement reflected growing international acceptance of the crackdown on Egypt's opposition and militants who have killed scores of policemen and soldiers since Morsi's overthrow. The crackdown, which has left at least 1,400 people dead, had tested Egypt's ties with the United States, which temporarily froze part of its annual $1.3 billion military aid in 2013.
Baird praised on Thursday "the significant leadership that the new government of Egypt is taking first in confronting the terrorist acts of the Muslim Brotherhood."
The Brotherhood, once Egypt's largest political movement and the winner of several elections, denies it resorts to violence.
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