Kagan, 50, the White House solicitor general and President Barack Obama's nominee to replace retiring Justice John Paul Stevens, said in her opening statement the nation's highest court promises "nothing less than a fair shake for every American."
"What the Supreme Court does is to safeguard the rule of law through a commitment to even-handedness, principle and restraint," she said.
The first day of her hearing before the Judiciary panel lasted for about four hours, with panel members staking their position before Kagan addressed the committee.
She was introduced by Sens. John Kerry and Scott Brown, a Democrat and a Republican.
After swearing her in, committee Chairman Patrick Leahy of Vermont, told Kagan, "Now the floor is yours."
Senators will begin questioning Kagan Tuesday.
Kagan said it was an honor to be nominated to replace Stevens on the court, expressing regret that she wouldn't be serving with him.
"I hope I will approach each case with his trademark care and consideration, listen with an open mind, striving as conscientiously as he to render impartial justice."
Every time she argued before the court she always came away with the sense of commitment each justice has to reason and principle.
"For this reason, the Supreme Court is a wondrous institution," Kagan said.
But her work in the legislative and executive branches showed the need for the court to be "modest," Kagan said, "properly deferential to the decisions of the American people and their elected representatives."
"The Supreme Court ... has the responsibility of ensuring that our government never oversteps its proper bounds or violates the rights of individuals," she said. "But the court must also recognize the limits on itself and respect the choices made by the American people."
"No one has a monopoly on the truth or wisdom," she said.
If confirmed, she said she could pledge no more than to remember and abide by the lessons she learned, and listen to every party before the court and her colleagues.
"I will work hard," she said, "and I will do my best to hear every case impartially, modestly, with commitment to principle and in accordance with (the rule of) law."
Leahy urged Kagan to "engage with the committee" and warned committee members about questioning Kagan's integrity.
"I reject the ideological litmus test that some from the right and left would apply to Supreme Court nominees," Leahy said.
Republican senators, meanwhile, tried to paint Kagan as having a thin judicial resume -- she has never been a judge -- and they warned against a judicial activist who would legislate from the bench.
Sen. Jeff Sessions, R-Ala., the committee's ranking Republican, drew attention to Kagan's lack of judicial experience.
"She has numerous talents and many good qualities," Sessions said, but "lacks real legal experience" because she hasn't practiced law, never tried a case before a jury and argued her first appellate case "just nine months ago."
Addressing concerns about possible activism, Sessions said the U.S. legal system must be a "check on (government) overreach, not a rubber stamp. A judge's role is "to fairly settle dispute of law, not set policy."
Sen. Lindsey Graham, R-S.C., said a Supreme Court justice must put aside a political agenda when on the bench.
"It's OK to be liberal. It's OK to be conservative," Graham said. "But when it comes time to be a judge, you've got to make sure you understand the limits that that position places on any agenda, liberal or conservative."
If confirmed, Obama's second Supreme Court nominee would be the fourth female justice and third woman sitting on the court, joining Ruth Bader Ginsburg and Sonia Sotomayor.