In a report to the UN Security Council, Secretary-General Annan said on Thursday that the prolonged period of relative quiet was followed by several attacks.
He highlighted the 9 January attack by Hizb Allah fighters against an Israeli patrol and Israel's attack that killed a French UN observer and wounded a Swedish observer.
Another damaging incident occurred on 17 January when a Hizb Allah roadside bomb damaged an Israeli military vehicle used for demining explosives in the disputed Shebaa Farms area, he said.
"The resumption of military measures, for which Hizb Allah took credit, asserting its claimed prerogative to resist Israeli occupation of Lebanese territory by force, was disturbing," Annan said.
Israel entered Lebanon in 1978 and launched a full-scale invasion in 1982. From 1985 until its withdrawal in May 2000, Israel occupied part of southern Lebanon.
The UN boundary, or Blue Line, is not a proper border and was drawn by the United Nations to mark Israel's withdrawal.
Israel captured the Shebaa
Farms in the 1967 war
The Shebaa Farms area on the foothills of Mount Hermon was captured by Israel when its forces seized Syria's Golan Heights in the 1967 Middle East war.
The United Nations determined that the area belongs to Syria, and that Syria and Israel should negotiate its fate. But Lebanon, backed by Syria, claims the area.
Annan said Lebanon's position that the Blue Line is not valid in the Shebaa Farms area is not compatible with UN Security Council resolutions.
He called on the Lebanese government to heed the council's repeated calls to respect the Blue Line "in its entirety".
The secretary-general said he was also "greatly troubled by the disregard shown for the safety and security of the unarmed United Nations military observers evidenced by the actions" of Israel's military forces on 9 January.
He urged both sides to ensure that UN personnel are not targeted.
Israeli violations of Lebanese airspace also continue to be a matter "of significant concern", he added.
"As long as Israel carries on with its policy of overflying Lebanon whenever it sees fit to do so, it risks provoking retaliatory acts from the Lebanese side," he said.
The secretary-general said Hizb Allah's launch of a drone into Israel was also "a regrettable development, an activity sure to raise tensions and to increase the prospects for military confrontation".
Annan said "rocket-firing incidents perpetrated by individuals allegedly affiliated with Palestinian militant factions demonstrated the volatility of the sector".
Annan wants the work of UNIFIL
to be extended
While none of the incidents resulted in a military escalation, he said, "this type of incident poses a great risk to stability in the area".
Annan noted that in private and public forums Israel and Lebanon have declared their desire to avoid confrontation, and he urged them to live up to their commitments and "do their utmost to adhere to a course favouring peace and security".
Because of the volatility along the boundary, the secretary-general recommended that the mandate of the 2000-strong UN Interim Force in Lebanon, known as UNIFIL, which patrols the Blue Line, be extended for six months until 31 July.