Hagel, who has reached out to all 100 senators, also was meeting with Sen. Susan Collins, R-Maine, on Tuesday.
Schumer met with Hagel Monday afternoon at the White House and then spoke to Obama in the Oval Office, according to a Senate aide. The New York senator telephoned Hagel Tuesday morning to tell him of his support.
Schumer said Hagel told him that he backs all steps necessary, including the use of military force, to stop Iran from obtaining a nuclear weapon. Schumer also said Hagel told him that he has always supported Israel's right to retaliate militarily against attacks by Hezbollah or Hamas, two groups he considers terrorist organizations.
Schumer said Hagel also provided assurances on gay rights and abortion rights for members of the military.
"I know some will question whether Senator Hagel's assurances are merely attempts to quiet critics as he seeks confirmation to this critical post. But I don't think so," Schumer said. "Senator Hagel realizes the situation in the Middle East has changed, with Israel in a dramatically more endangered position than it was even five years ago. His views are genuine, and reflect this new reality."
Boxer said Hagel assured her that he would carry out Obama's policies "without reservation." Schumer said the Pentagon nominee mollified him on the issue of unilateral sanctions on Iran, which Hagel has said in the past were ineffective.
"In our meeting, however, Senator Hagel clarified that he 'completely' supports President Obama's current sanctions against Iran. He added that further unilateral sanctions against Iran could be effective and necessary," the New York senator said.
Boxer said Hagel, like others, has evolved on gay rights. She said that he promised to meet with her on issues such as sexual assault in the military.
Responding to the criticism of Hagel, Boxer said, "I feel people are being very unfair to Chuck Hagel."