In a statement, the Foreign Ministry on Saturday said that Billstrom had a conversation with more than 20 ambassadors of the Organization of Islamic Cooperation (OIC) member states in the capital Stockholm on Friday.
He said they have had "a fruitful and constructive meeting," adding he is keen to continue "open and constructive dialogue."
"Restoring trust and confidence takes time. I will devote a substantial part of this electoral period to strengthening relationships with Muslim countries," Billstrom added.
He said his government "strongly rejects" the burnings of copies of holy scriptures, adding that the Justice Ministry has initiated an analysis and is working on the terms of reference for an inquiry to review the Public Order Act.
"I intend to travel to OIC countries, and Sweden will host discussions and dialogues in connection with the UN General Assembly in New York in September," he added.
Also speaking to the Swedish news agency TT after the meeting, Billstrom said that the meeting was "a good opportunity to explain the government's approach and its constitutional freedoms" in the face of the incidents, Radio Sweden reported.
Earlier this week, Justice Minister Gunnar Strommer said that one potential solution to prevent the desecration of the Quran could be to use emergency powers that the government can wield under the Public Order Act.
Jakob Forssmed, the Swedish social affairs minister, also had a meeting with representatives from different faith-based organizations in the Swedish capital on Friday.
Recent months have seen repeated acts of Quran burning, desecration, or attempts to do so by Islamophobic figures or groups, especially in northern European and Nordic countries.