Hagel, on his first visit to Israel as Pentagon chief, also declared that it is Israel's right to decide for itself whether to attack Iran to stop it from building a nuclear bomb.
Those two messages appeared to form the foundation of Hagel's effort to improve U.S. relations with Israel, which have been strained in recent years by obstacles to reviving Israeli-Palestinian peace talks and by the threat of an Iranian bomb.
Later, Hagel was flown in an Israeli Army UH-60 Black Hawk helicopter over northern Israel to view the Golan Heights, an area along the Syrian border that Israel captured during the 1967 Six-Day War.
The flight appeared to be aimed in part at impressing upon Hagel the narrow reaches of Israel and its vulnerability to troubled areas like Syria, which is in the midst of civil war.
An Israeli Defense Forces information packet provided to those who took the flight with Hagel noted that "the State of Nebraska is nine times the State of Israel." Hagel is a former two-term Republican senator from Nebraska.
At a joint news conference with Hagel prior to their flight, Israeli Defense Minister Moshe Yaalon, said security in the Golan Heights is one of Israel's chief worries about Syria's turmoil.
In his appearance with Yaalon, Hagel was asked whether he believes it would be advisable for Israel to attack Iran on its own.
"That calculation has to be made by" Israel, he replied after noting, "Israel is a sovereign nation; every sovereign nation has a right to defend itself."
Hagel did not mention a concern that U.S. officials have voiced in the past, namely, that an Israeli strike would run the risk of igniting a wider war that could draw in the United States.
As evidence of Washington's commitment to preserving Israel's so-called qualitative military edge in the Mideast, Hagel said the U.S. will permit Israel to buy various new weapons, including U.S. missiles and advanced radars for its strike aircraft.
"We are committed to providing Israel with whatever support is necessary for Israel to maintain military superiority over any state or coalition of states and non-state actors," Hagel said.
Yaalon was asked about reports that the Syrian government has used chemical weapons in its struggle against rebel forces.
He did not specifically say whether Israel believes such weapons have been used, but he said that Syria must not cross the "red line" of allowing any chemical weapons to fall into the hands of what Yaalon called "rogue elements."
He said that "red line" has not yet been crossed.