At that time, the senate leader said lawmakers should have a better sense of how the U.S. economy is faring and how the virus is evolving.
Administration officials have said that the “shape” of the next relief package would be conditional upon the U.S. economic recovery.
McConnell also has said lawmakers need to take time to assess what worked, and what didn’t, from prior legislation.
One item that is being debated among lawmakers is how to continue supporting the many Americans who have been furloughed, laid off or had their hours reduced as a result of the pandemic. About 47 million people have filed new unemployment claims since mid-March.
McConnell said on Tuesday that having basic protections for these individuals is “extremely important,” though what form those protections take has been a source of division among Republicans and Democrats.
McConnell previously said he and the Trump administration are not in favor of including an extension of the $600 unemployment benefit expansion, which he said has deterred workers from returning to their jobs.
Some Democrats are looking to extend the measure beyond its scheduled expiration in July.
But U.S. Treasury Secretary Steven Mnuchin has confirmed the next stimulus package would be “jobs-focused,” prioritizing “bringing back” positions.
The administration has backed what it calls a “back-to-work bonus” as an alternative, which would provide an incentive for individuals to reenter the marketplace.
Another priority for lawmakers is adding in liability protections, which would be extended beyond businesses, McConnell said.
Some other policies that the administration is believed to be considering include a payroll tax cut, a reduction in the capital gains tax rate, an expansion of full, immediate expensing and a return of the full deduction for business meals and entertainment.
President Trump has also suggested that there could be another round of stimulus checks on the way for Americans.
FOX Business’ Blake Burman contributed to this report.