McConnell and Senate Democratic leader Chuck Schumer, were among the few senators in the chamber amid stay-home orders that have shut Washington, and the US.
Two conservative Republicans, Senator Mike Lee and Senator Rand Paul, voiced opposition, but they did not halt passage.
Lee said it was "unacceptable" that the full Senate was not present and voting in the pro forma session. Paul echoed that concern as they called Congress back to session.
The agreement was announced by Schumer earlier and Trump tweeted his support, saying he'll sign the bill if passes both chambers. McConnell swung behind it as well.
Schumer said the bill was made "better and broader" after Democrats forced the inclusion of money for hospitals and testing..
The President said he was open to including in a subsequent virus aid package fiscal relief for state and local government — which Democrats had wanted for the current bill — along with infrastructure projects.
Most of the funding, US$331b, would go to boost a small-business payroll loan programme that ran out of money last week. An additional US$75b would be given to hospitals, and US$25b would be spent to boost testing for the virus, a key step in building the confidence required to reopen state economies.
- AP
