U.S. Senate Republicans and the Trump administration have reached an agreement in principle on the next COVID-19 relief package, Senate Majority Leader Mitch McConnell said Thursday.

McConnell said Senate Republicans will release their proposal, which will focus on kids, jobs and healthcare, next week as the Trump administration has requested additional time to review the fine details.

"We need to get Americans back to work and school while continuing to fight for our nation's health. That is what CARES 2 is designed to do," he said.

U.S. Congress passed the 2.2-trillion-U.S.-dollar CARES Act, or the Coronavirus Aid, Relief, and Economic Security Act, in March to provide fiscal aid for households, businesses and healthcare providers, but some key provisions in the act are set to expire at the end of this month.

U.S. Treasury Secretary Steven Mnuchin said on Thursday that the administration will not extend the extra weekly 600-dollar unemployment benefits under the CARES Act, but will replace it with a roughly 70 percent match of a worker's wages before they were laid off.

"As we've said before, we're not going to continue within its current form because we're not going to pay people more money to stay at home than work, but we want to make sure that the people that are out there that can't find jobs do get a reasonable wage replacement, so it will be based on approximately 70 percent wage replacement," Mnuchin said in an interview with CNBC.

Mnuchin also confirmed that the payroll tax cut, which President Donald Trump has repeatedly pushed for, will not be included in the relief package.

"The Democrats have stated strongly that they won't approve a Payroll Tax Cut (too bad!). It would be great for workers. The Republicans, therefore, didn't want to ask for it. Dems, as usual, are hurting the working men and women of our Country!" Trump tweeted Thursday, blaming Democrats for sinking the proposal.

U.S. lawmakers are under immense pressure to craft a new fiscal package as a resurgence of COVID-19 cases across the country threatens to derail the nascent economic recovery.

The number of COVID-19 cases in the United States surpassed the four-million mark Thursday with more than 143,000 deaths, according to Johns Hopkins University.