White House economic adviser Larry Kudlow on Thursday said he expects the U.S. unemployment rate to return to single-digit levels as early as this month and growth in the third quarter should be 20% or more as the economy recovers from the recession triggered by the coronavirus pandemic.

"The key point that I would make is the economy is rebounding, it looks like a V-shaped recovery and the recent news now is even better than it was a month ago," Kudlow said in a virtual appearance at a conference hosted by the Council of the Americas.

His optimistic outlook contrasts with remarks from several Federal Reserve officials who said this week that the rebound is slowing after a resurgence in coronavirus infections and that the U.S. economy cannot fully recover until the virus is under control.

The number of Americans seeking unemployment benefits dropped below one million last week for the first time since mid-March, but economists said that was likely caused by the expiration of a $600 weekly supplement, which discouraged some people from filing claims.

Kudlow cited the drop in claims as a sign that the labor market is recovering. Asked if the economy needs another round of stimulus, Kudlow said recent executive actions taken by President Donald Trump should provide some relief.

These extend enhanced unemployment benefits at a reduced level of up to $400 a week and continue a freeze on student loan interest and payments. But several economists said this week that Trump's actions, which are likely to face legal challenges, would have a minimal impact on the economy.

Kudlow said bipartisan efforts to provide help for small businesses and more direct payments to households could also help, but noted that negotiations with Democrats were at a "standstill." 

Separately, Kudlow said Trump's efforts to give workers a break on payroll taxes will apply to self-employed individuals, but gave no other details.

Kudlow, speaking to reporters at the White House, said a "technical change" would have to be issued to Trump's memorandum released on Saturday calling for payroll taxes to be deferred amid the COVID-19 pandemic in order to include people who work for themselves.

In another interview with CNBC, Kudlow also said Trump opposes “voting rights” plans backed by Democrats in the next coronavirus relief bill. 

“That’s not our game, and the president can’t accept that kind of deal,” the director of the National Economic Council continued. “So, we’ll wait and see on the negotiations. Treasury Secretary [Steven] Mnuchin is working on that, but so far it’s a stalemate.”