The STL is investigating the 2005 assassination of former Lebanese Prime Minister Rafik Hariri. Four members of Hezbollah are accused of playing a role in the assassination, allegations the Shiite movement denies.
The tribunal last year released the names of suspects -- Salim Jamil Ayyash, Mustafa Amine Badreddine, Hussein Hassan Ainessi and Assad Hassan Sabra -- who are wanted for the bombing attack in which 22 people died.
A source in the Lebanese government told The Daily Star newspaper that STL chief David Baragwanath was outraged that newspaper al-Akhbar leaked witness information.
"Baragwanath vowed to conduct a serious and effective investigation until it is clear who is behind these leaks, and punish them," the source said on condition of anonymity.
The STL said it was concerned about the safety of tribunal witnesses.
The trial was delayed in February following a challenge by the defense team in the case. The STL said the trial could begin in late 2013, though defense teams said it was too early to specify a trial date.