She said the president and first lady will visit Pennsylvania on Tuesday.
The alleged gunman, Robert Bowers, has appeared in court in a wheelchair.
The mass shooting at the Tree of Life Synagogue is being called the worst anti-Semitic attack in US history.
What did the White House say?
“The president is not responsible for these acts,” Mrs Sanders said repeatedly during Monday’s news conference when a reporter put it to her that Mr Trump’s rhetoric could have played a part in the Pittsburgh attack, or a recent mail bomb scare.
“I think it’s irresponsible to blame the president and members of his administration for those heinous acts.”
The press secretary’s voice cracked with emotion as she spoke of how the president “adores” Jewish Americans.
The suspect was not a Trump supporter – he accused the president in online posts of doing nothing to stop an “infestation” by Jews.
Mr Trump has condemned the shooting, saying there ought to be no tolerance for anti-Semitism.
What have Jewish community members said?
A Jewish social justice organisation accused the president in an open letter of giving succour to white nationalists.
“President Trump, you are not welcome in Pittsburgh until you fully denounce white nationalism,” Bend the Arc said in the letter, which now has more than 43,000 signatures.
It noted the president has frequently criticised immigrants and Muslims.
However, Rabbi Jeffrey Myers, who leads a congregation at the Tree of Life synagogue, said the president was always welcome.
“I’m a citizen, and he’s my president, he’s certainly welcome,” Mr Myers said on ABC’s Meet the Press.
The alleged gunman was ranting against Jews even as he was treated by Jewish medical staff at the hospital for wounds he received in a gun battle with police.
Jeffery Cohen, president of Allegheny General Hospital, told WTAE-TV: “He’s taken into my hospital and he’s shouting ‘I want to kill all the Jews!’
“And the first three people who are taking care of him are Jewish. Ain’t that a kick in the pants?”
Just before the attack, the alleged gunman railed on social media against a Jewish refugee relief organisation.
The suspect accused the Hebrew Immigrant Aid Society (HIAS) of bringing violent “invaders” into the country.
Mark Hetfield, head of HIAS, said on Monday: “President Trump didn’t mention that.
“Hateful words always lead to hateful acts. And that’s exactly what happened here. Words matter. And they especially matter when they come from the president of the United States.”
Who were the victims?
Eight men and three women ranging in age from 54 to 97 were killed at the Tree of Life synagogue.
Several had attended the place of worship since childhood.
Two brothers, and a husband and wife are among the dead.
Joyce Fienberg, 75
Richard Gottfried, 65
Rose Mallinger, 97
Jerry Rabinowitz, 66
Cecil Rosenthal, 59
David Rosenthal, 54, brother of Cecil
Bernice Simon, 84
Sylvan Simon, 86, husband of Bernice
Daniel Stein, 71
Melvin Wax, 88
Irving Younger, 69
The first funerals will be held on Tuesday, for Cecil and David Rosenthal.
What happened?
Mr Bowers allegedly stormed the Tree of Life temple in the Squirrel Hill neighbourhood of Pittsburgh, shouting: “All Jews must die!”
The FBI says three handguns and an AR-15 rifle, used in many of the nation’s mass shootings, were recovered at the scene.
He owned all the weapons legally, officials say.
Survivor Barry Werber, 76, said he hid in a dark storage closet during the rampage.
“I don’t know why he thinks the Jews are responsible for all the ills in the world, but he’s not the first and he won’t be the last,” Mr Werber told AP news agency.
“Unfortunately, that’s our burden to bear. It breaks my heart.”
A Muslim fundraiser to help victims of the shooting was launched with a goal of $25,000 – it has so far amassed more than $150,000 in donations.