Sanders, speaking to CNN's Dana Bash after exiting Tuesday night's State of the Union address, said Clinton's jabs at his record on guns and health care were more motivated by fear of his strength as a candidate.
In a new advertisement released during President Barack Obama's speech, Clinton argued voters must "pick a side" between the gun lobby and the White House.
"I stand with the President on gun issues," Sanders said when shown the advertisement.
Clinton and her allies having worked to portray Sanders in a different light, including highlighting the Vermont senator's past votes to support immunity for gun companies.
"There are some parts of that bill are right, and there are some parts of that bill that are wrong, and I am, as I said several months ago, willing to re-look that," Sanders said, refusing to say he regrets the vote.
"Secretary Clinton, obviously now, sees herself in trouble," Sanders said, pointing to his recent surge in polls.
The Vermont senator also replied to a criticism from Chelsea Clinton, who charged that his health care plan would empower Republican governors who could limit Medicare coverage.
"As much as I admire Chelsea, she didn't read the plan," Sanders said, arguing for his Medicare-for-all program. "And where she is absolutely wrong: This is a plan that works in 50 states in this country, whether you have conservative Republicans or progressive Democrats. It's a national program."
Sanders also reiterated to Bash on Tuesday evening that before the Iowa caucuses he plans to release a detailed tax plan to pay for his proposals -- which are now less than three weeks away.