The news conference, which focused on international and military affairs, came a day after NBC News' "Commander-in-Chief Forum," where both candidates were asked about foreign policy and veterans' issues.
"Last night was yet another test, and Donald Trump failed yet again," Clinton said. "We saw more evidence that he is temperamentally unfit and totally unqualified to be commander in chief. He trash-talked American generals, saying they've been 'reduced to rubble.' "
In NBC's forum, Trump said that he'd fire current generals if he becomes president, as they had been "reduced to a point where it's embarrassing for our country."
Clinton said Trump disparaged the sacrifices of distinguished service members.
She also homed in on Trump's position on Russian President Vladimir Putin, saying that past presidents, including Republican Ronald Reagan, would be astonished at the Republican candidate's comments. Trump on Wednesday pointed to Putin's 82 percent approval rating, calling him more of a leader than President Barack Obama.
"That is not just unpatriotic and insulting to the people of our country, as well as our commander in chief — it is scary," Clinton said. "Because it suggests he will let Putin do whatever Putin wants to do, and then make excuses for him."
Trump has said he doesn't want to give details on his specific plan to defeat ISIS because he doesn't want to broadcast it to America's enemies, a strategy Clinton called "dangerous" and "disqualifying."
"We would leave a certain group behind and you would take various sections where they have the oil," Trump said, to prevent groups like ISIS gaining control of the resource.
Clinton on Thursday reiterated her opposition to sending a big contingent of troops on the ground in Iraq and Syria, saying it would fulfill ISIS' wish for a ground war with America. She also called Trump's rhetoric a "gift for ISIS," in reference to the Time article, "Why ISIS supports Trump."
"The United States of America does not invade other countries to plunder and pillage," Clinton said. "We don't send our brave men and women around the world to steal oil. And that's not even getting into the absurdity of what it would involve — massive infrastructure, large numbers of troops, many years on the ground — of course, Trump hasn't thought through any of that."
Clinton also chastised Trump for hinting about things he learned in classified intelligence briefings he has received as the nominee.
"I would never comment on any aspect of an intelligence briefing I received," she said.
Trump's campaign responded to Clinton's criticisms, calling the attacks dishonest, desperate, and "unhinged."
"Last night Hillary Clinton again failed the commander-in-chief test, where she was unable to answer for her terrible foreign policy judgment, mishandling of classified information and claims that the VA wait time scandal was overblown," said Jason Miller, Trump's senior communications advisor. "Her claim that no lives were lost in Libya was an insult to the memory of the four brave Americans who died in Benghazi."
The Democratic nominee said she will convene a meeting on Friday of bipartisan national security leaders and experts, including Michael Chertoff, former secretary of homeland security, in an effort to send a message to those who would wage attacks on the U.S.
"We should make it a top priority to hunt down the leader of ISIS … and bring him to justice, just as we did with Osama Bin Laden," Clinton said.
Clinton, who had been criticized by Trump for not holding a news conference since Dec. 5, also took reporters' questions in an informal session on her plane on Tuesday.
— Reuters contributed to this report.