"There is a difference between spying carried out by people who have been detected and detained and detectors and spying equipment which have been found during last week," he told reporters in Spain where he is on a state visit.
"Both these spy networks and these means of spying are a clear violation of Israel of (U.N.) Resolution 1701, even more so than the violation of Lebanese air space that is routinely carried out by Israel."
Resolution 1701 calls for the removal of weapons in southern Lebanon from the hands of everyone except the Lebanese army and other state security forces.
A Lebanese military source said Sunday that three "Israeli spying devices" which monitored communications in Lebanon had been destroyed near the border with Israel, two of them blown up by the Israeli army.
Hizbullah said it discovered a spying device installed by Israel on a cable between the villages of Houla and Mais el-Jabal after the 2006 war between it and the Jewish state.
It said the Lebanese army and troops from the United Nations Interim Forces in Southern Lebanon (UNIFIL) later discovered the two other devices.
More than 70 people have been arrested this year in Lebanon on suspicion of spying for Israel.
Suleiman met with Spanish Prime Minister Jose Luis Rodriguez Zapatero and King Juan Carlos during his three-day visit to Spain, which wraps up on Wednesday in Barcelona.
About 1,000 Spanish soldiers are deployed with UNIFIL, which was set up in 1978 to monitor the border between Israel and southern Lebanon.
The force was considerably beefed up in the wake of the 2006 war between Israeli forces and Hizbullah and it now has about 13,000 soldiers from various nationalities.
Suleiman said the UNIFIL forces can only leave if Israel removes its army from three locations in the south of Lebanon which he said it is occupying in another violation of U.N. resolution 1701.
"The withdrawal of United Nations forces from southern Lebanon depends solely on the re-establishment of stability in the region," he said.
"When, and only when, Israel stops occupying this Lebanese territory can the Security Council of the United Nations take the decision to withdraw its security forces from southern Lebanon."(AFP)