White House economic adviser Larry Kudlow said on Sunday he would not rule out anything in a new relief bill to ease the "tremendous hardships" of the coronavirus outbreak, including more money for state and local governments and small businesses.

More than 30 million Americans have joined the unemployment benefit rolls over the past six weeks and lawmakers on Capitol Hill are discussing a fourth coronavirus relief bill.

Democrats are pushing for additional aid to help cities and states cope with lost revenue from a shut-down economy and some governors have warned of massive layoffs if they fail to get it.

Some advisers to Republican President Donald Trump have said the need for another stimulus bill is not yet clear. But Kudlow said "there may well be additional legislation" as officials study how the billions included in the last bill take effect.

"We know the economy is still in a terrible, contractionary phase, tremendous hardships, everywhere," Kudlow said on CNN's "State of the Union."

"We're trying to work through this. I don't want to rule in or out anything right now. We are in discussions internally and with leading members of Congress."

Congress has not met in regular session since March, though it has passed major coronavirus relief bills worth nearly $3 trillion. House Speaker Nancy Pelosi, a Democrat, said money for states and cities would be the core of the next legislative package Democrats draft.

Trump has considered linking such aid to sanctuary cities' immigration policies, Kudlow said.

New Jersey Governor Phil Murphy said on Sunday federal help to states that have taken a big revenue hit from coronavirus would make a "huge difference."

"This is about firefighters, police, EMS, teachers at the point of attack. We're already seeing some layoffs in New Jersey," Murphy said on "Fox News Sunday." "We need a big slug of federal, direct cash assistance."

All 50 states are suffering from the lack of revenue over the past two months, Illinois Governor J.B. Pritzker said in response to Trump's argument that states with budget woes before the coronavirus outbreak should not get bailed out.

"Coronavirus has caused that. All of us are having to spend more on social services and healthcare to take care of people," Pritzker said on CBS' "Face the Nation."

Kudlow said authorities need to see the results of the previous funding efforts before deciding on the next steps.

"Then we'll see, we will see in a couple of weeks, what needs to be done and perhaps how to do it," Kudlow said.

Kudlow was asked whether more aid would be given to small businesses.

"It may be," Kudlow said. "We haven't made a decision yet."