Trump's ban barred all refugees and travelers from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen from entering the US.
In a brief submitted to the US Court of Appeals for the Ninth Circuit, the former top officials argued that the executive order signed by Trump on January 27 was "ill-conceived, poorly implemented and ill-explained."
Trump's ban barred all refugees and travelers from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen from entering the United States.
On Friday, following a lawsuit filed by the state of Washington challenging the ban, a federal judge in Seattle temporarily suspended Trump's order pending a wider legal review.
The Trump administration appealed over the weekend to the Ninth Circuit court, where a flurry of legal filings were flooding in early Monday.
They included a brief from the prominent Democrats, who included Kerry, Albright and several top aides to ex-president Barack Obama.
Among them were national security advisor Susan Rice, CIA chief and defense secretary Leon Panetta, and homeland security chief Janet Napolitano.
"We view the Order as one that ultimately undermines the national security of the United States, rather than making us safer," they argued.
"Reinstating the Executive Order would wreak havoc on innocent lives and deeply held American values."
Specifically, the brief said Trump's travel ban could endanger US troops in the field and disrupt counterterrorism cooperation.
It also feeds Islamic State group propaganda that the United States is at war with Islam, it said.
Trump has defiantly defended his position and launched fiery tweets attacking the judge who suspended the travel ban.
"Just cannot believe a judge would put our country in such peril. If something happens blame him and court system. People pouring in. Bad!" he said in a post on Sunday.