"Part of the constitution needs to clearly address the issue of freedom of the media," Reinfeldt said during a press conference with Gül in Stockholm.
The Turkish parliament formed a special committee in May last year to draft a basic law that would replace the current constitution dating back to a military coup in 1980.
Turkey is the leading jailer of journalists worldwide, imprisoning even more than China or Iran, according to an October report by the US-based Committee to Protect Journalists.
Many journalists were being detained under the country's broadly defined terrorism laws, according to Reinfeldt.
"We hope that a full judicial package adopted by the government will lead to a more narrow definition of terrorism," he said.
"This is also an issue of how it is used by free-standing courts. But we have discussed it and I think reform is now on its way," he added.
But the Turkish leader said Europe's high standards for freedom of speech and other human rights could make countries vulnerable to terrorism.
"Democracy, human rights, freedom of expression standards in Europe are very high. Unfortunately at times, terrorism exploits that," Gül said.
"Those people who have something to do with terrorism... make use of this superiority of European democracies, and turn it into a weakness in a way," he added.
Turkish intelligence services and security forces were "always in close communication" with their European counterparts and shared information when necessary, he noted.
Reinfeldt also emphasized his hope to see long-stalled negotiations on Turkey's application for membership in the European Union get a fresh start.
"We hope to be able to open a new negotiation chapter this spring," said Reinfeldt, explaining that Turkey had made progress on the issue of minorities rights.
"Our discussions about the rights of Kurds have clearly developed over the years."
Gül explained that some EU member states have created obstacles for Turkey's EU membership bid, but asserted that "that's not a reason to give up on membership".
Gül's visit to Stockholm will also resulted in the signing of a strategic partnership agreement on green energy technology cooperation between Sweden and Turkey.