WASHINGTON, Oct. 19 (Xinhua) -- U.S. House Speaker Nancy Pelosi and Treasury Secretary Steven Mnuchin on Monday made progress on the next round of COVID-19 relief package, said Drew Hammill, Pelosi's spokesman and deputy chief of staff.

"The Speaker and Secretary Mnuchin spoke at 3:00 p.m. (1900 GMT) today for approximately 53 minutes. In this call, they continued to narrow their differences," Hammill said in a tweet Monday afternoon.

The spokesman noted that Pelosi has tasked committee chairs to reconcile differences with their Republican counterparts on key areas, and the two principals will speak again on Tuesday.

"The Speaker continues to hope that, by the end of the day Tuesday, we will have clarity on whether we will be able to pass a bill before the election," Hammill said.

The conversation follows Pelosi's remarks on Sunday that White House and congressional lawmakers must reach an agreement in 48 hours if they want to pass a new relief package before the presidential election in early November.

"The 48 only relates to if we want to get it done before the election, which we do," Pelosi said in an interview with ABC News.

During a virtual conference hosted by the Milken Institute last week, Mnuchin, however, said that it would be difficult for the White House and Democrats to reach a deal on a comprehensive COVID-19 relief package before the election, as the two sides were still far apart on certain issues.

A recent call on Saturday night between the two sides resulted in "some encouraging news on testing," according to Hammill.

Despite the progress, lawmakers remain deadlocked on the new relief bill over two months after the extra 600-U.S.-dollar per week federal unemployment benefits -- part of a 2-trillion-dollar relief package approved by Congress in late March -- expired at the end of July.

Earlier this month, the Democrats-controlled House passed a 2.2-trillion-dollar bill, while the White House most recently offered up to nearly 1.9 trillion dollars. Some Senate Republicans even insisted a figure below 1 trillion dollars.

Economists, as well as Federal Reserve officials, have repeatedly argued that more fiscal relief is needed to sustain the economic recovery, warning of dire consequences if further fiscal support is not provided in time.