"It is not legally possible to shut down the Internet and such platforms (as Twitter)," Abdullah Gul told reporters in Ankara before leaving for an official visit to the Netherlands.
"I believe this problem will be over soon," he said.
"This is of course an unpleasant situation for such a developed country as Turkey, which has weight in the region and which is negotiating with the European Union. Therefore, it will be overcome soon."
The president also confirmed that the US-based social media giant had hired a lawyer in Turkey for negotiations with the authorities.
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Gul, a frequent social media user, took to Twitter on Friday to denounce the government's ban hours after the network went dark, becoming the highest-level leader in the country to circumvent the block, along with some ministers.
The Twitter ban was instituted late Thursday after Prime Minister Recep Tayyip Erdogan threatened to "wipe out" the social network.
Gul, who hails from Erdogan's Islamic-rooted Justice and Development Party (AKP), has emerged as a more conciliatory leader than the Turkish premier, who has been in power since 2003.
Government officials said authorities blocked access to Twitter because the service ignored "hundreds of court orders" to remove some links deemed illegal.
Critics however claim it was an attempt to hush up corruption allegations ensnaring Erdogan and his allies ahead of key local elections on March 30.
Audio tapes allegedly depicting Erdogan involved in massive corruption have flooded social media networks including Twitter almost daily.
Erdogan has dismissed most of the audio recordings as a "vile montage" put together by his political rivals.