Treasury Secretary Steven Mnuchin said Thursday that people will start getting relief checks within three weeks, as the country reels from the coronavirus pandemic.

Mnuchin spoke to CNBC the morning after the Senate passed a $2 trillion stimulus package intended to blunt economic damage from the spread of the coronavirus. The House is expected to vote on the legislation Friday.

The massive relief bill offers direct cash payments of up to $1,200 for individuals and $2,400 for couples, with $500 added for every child, based on 2019 tax returns for those who filed them and 2018 information if they have not. The benefit begins to phase out for individuals making $75,000 in income and ends completely for those making $99,000 or more.

"Most of these will be direct deposit," Mnuchin said. "It will be within three weeks."

"We're determined to get money in people's pockets immediately," he said.

The payments would come amid a historic spike in jobless claims: Weekly initial unemployment claims totaled nearly 3.3 million, by far a record, according to data released Thursday.

"I just think these numbers right now are not relevant," Mnuchin said when asked about that staggering figure. "Whether they're bigger or smaller in the short term ... the good thing about this bill is, the president is protecting these people."

White House spokesman Judd Deere said in a statement later Thursday that President Donald Trump is grateful for the "enormous sacrifices" Americans are making in the face of the pandemic.

"The large increase in unemployment claims is just one of the many reasons why President Trump committed weeks ago to take care of all Americans, including affected industries and small businesses, so that we emerge from this challenge stronger and with a prosperous and growing economy."

Deere added that the White House believes the House should pass the stimulus bill "without delay."

Market futures turned positive shortly after the jobless numbers were announced. After shedding trillions of dollars in value for weeks, stocks rose Thursday for the third straight session, as lawmakers rushed to provide relief for ailing industries and individuals.

Trump has also strongly signaled that he wants the economy "reopened" as soon as possible. Trump suggested repeatedly this week that areas of the country with comparatively low numbers of confirmed COVID-19 cases could allow businesses to reopen in just a few weeks, if not sooner.

But it's far from clear which states, if any, would agree to quickly loosen the extreme measures they have imposed to slow the spread of the disease.

Nearly every state in the country has declared a state of emergency amid the pandemic as confirmed cases continue to rise rapidly throughout the country – especially in "hot spots" such as New York and Washington. New states were ordering all residents to stay home as recently as Wednesday.