Senate Majority Leader Mitch McConnell said Tuesday the $367bn federal program green-lighted in March to help small businesses through the coronavirus crisis will need more money in a follow-up bill with an infusion of cash, which he hopes to pass through the Senate as early as Thursday.

Mr McConnell's statement Tuesday on providing more small business relief marks the first time he has commented on the substance of a follow-on bill to the $2.2trn "phase three" economic stimulus package passed in March, and could be a jumping off point for negotiations on a "phase four" package with Democrats and the White House.

“As the administration works to implement this historic legislation and push money out the door, Senate Republicans believe any potential further action will need to be tailored to the actual needs of our nation," Mr McConnell said. "One such need is already clear: The small-business Paycheck Protection Program needs more funding."

The majority leader's comments reflect Donald Trump's growing realization that the loan program, commonly referred to as PPP, will need an infusion of cash from Congress well before the eight weeks is up that it was previously projected to last.

"We're going to have to probably add more money to this to save and to keep our small businesses going and to keep the employees of those small businesses working," the president said at his daily coronavirus press briefing Monday.

The third coronavirus legislative response package, which Congress passed and the president signed into law last month, included more than $350bn in small business relief in the form of loans that could be forgiven up to 100 per cent if businesses meet certain payroll and operational requirements.

Mr McConnell hopes to fast-track approval in the Senate this week for billions of dollars more for the small business relief program, he indicated Tuesday.

"Congress needs to act with speed and total focus to provide more money for this uncontroversial bipartisan program," he said. "I will work with Secretary Mnuchin and [Minority] Leader [Chuck] Schumer and hope to approve further funding for [PPP] by unanimous consent or voice vote during the next scheduled Senate session on Thursday."

It is not yet clear whether Mr McConnell can pass such legislation without objection from senators. All it takes is one to delay passage, and Republican Senators Rand Paul of Kentucky and Mike Lee of Utah are always wary of passing bills with a large federal price tag without proper debate.

Spokesmen for Mr Paul nor Mr Lee could immediately be reached for comment.

Speaker Nancy Pelosi indicated late last week that small business relief was congressional Democrats' priority as well, and that negotiating a quick bill to provide more to PPP could delay discussions with Mr McConnell on other Democratic priorities, such as an infrastructure package.