"We see opportunity in the cease-fire, which has now been established in the eastern part of Ukraine, but we also see violations of the cease-fire and that it's a fragile situation," Jens Stoltenberg said.
On his first day in office, the 55-year-old Stoltenberg also welcomed the bombing campaign being waged by the United States, France, Britain and other NATO and non-NATO nations against Islamic State militants, who he said have committed "horrific atrocities" in Iraq and Syria.
He also said the alliance would react with an "open mind" if Russia were to seek to revive the NATO-Russia Council, which has virtually ceased to operate since Russia annexed the Crimean Peninsula in March.
A former two-term Norwegian prime minister, Stoltenberg became the 13th secretary-general in the trans-Atlantic organization's 65-year existence. Analysts predicted his consensus-building style would mean softer rhetoric than his predecessor, Denmark's Anders Fogh Rasmussen.
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To allies like Germany, the expectation of a dial-back of the rhetoric was one factor in Stoltenberg's favor.
Stoltenberg was unanimously chosen as Rasmussen's successor by NATO's policy-making North Atlantic Council in March. The choice won swift if tentative approval from Russian President Vladimir Putin, who had dealt with Stoltenberg when he headed a center-left government in Norway, a Russian neighbor.
"We have very good relations, including personal relations," Putin told Russian state television at the time.
Stoltenberg is the first secretary-general to hail from an alliance nation that borders Russia. He becomes NATO's highest-ranking civilian at a time when Western relations with Moscow are at their lowest ebb since the collapse of the Berlin Wall a quarter-century ago.