Coronavirus updates: New cases, deaths see double-digit increases in past week

California has been added to New York’s growing travel advisory list, Gov. Andrew Cuomo said Tuesday.

Forty-five states and territories now meet the travel advisory requirements, Cuomo said. Those who come to New York must quarantine for two weeks if they travel from areas with positive test rates above 10 per 100,000 residents over a one-week average, or an area with a 10% or higher positivity rate over a one-week average.

These are the states and territories on the list: Alaska, Alabama, Arkansas, Arizona, California, Colorado, Delaware, Florida, Georgia, Guam, Iowa, Idaho, Illinois, Indiana, Kansas, Kentucky, Louisiana, Maryland, Michigan, Minnesota, Missouri, Mississippi, Montana, North Carolina, North Dakota, Nebraska, New Mexico, Nevada, Ohio, Oklahoma, Puerto Rico, Rhode Island, South Carolina, South Dakota, Tennessee, Texas, Utah, Virginia, Wisconsin, West Virginia and Wyoming.

Connecticut, New Jersey, Massachusetts and Pennsylvania meet the criteria for the travel advisory list, but Cuomo said it’s not practical to enforce a quarantine with neighboring states. New Yorkers are discouraged from nonessential travel to those states.

ABC News’ Josh Hoyos contributed to this report.

Greece reported 1,259 new COVID-19 cases on Tuesday, a record 24-hour increase, surpassing the 935 new infections reported on Saturday, according to the National Public Health Organization.

The small Mediterranean country now has over 32,000 cases.

Twelve new deaths were reported on Tuesday, pushing Greece's fatality total to 593.

Meanwhile, Italy on Tuesday also reported a record 24-hour increase -- 21,994 newly diagnosed cases -- breaking a record set on Sunday, according to the Civil Protection Agency.

Italy now has more than 564,000 cases and at least 37,700 fatalities.

Walter Ricciardi, a top Italian physician and adviser to Health Minister Roberto Speranza, called for Naples and Milan to be locked down on Tuesday, saying "in Milan and Naples you can get COVID by walking into a bar or a restaurant or catching a bus."

ABC News’ Christine Theodorou contributed to this report.

White House coronavirus response coordinator Dr. Deborah Birx visited shops and restaurants in Bismark, North Dakota, on Monday, where she said she saw the lowest make use of anywhere she’s visited, local TV station KFYR-TV reported.

“There is not only evidence that masks work, there is evidence that masks used as a public health mitigation effort works,” Birx said, according to KFYR-TV.

North Dakota Gov. Doug Burgum is against a statewide mask ruling, instead leaving it up to local governments, KFYR said. In Bismark, the city commission is expected to vote on a mask order Tuesday night, according to KFYR.

The number of new cases of COVID-19 recorded across the United States has increased substantially, as has the number of new deaths from the disease, according to an internal memo from the U.S. Department of Health and Human Services that was obtained by ABC News on Monday night.

The memo, which is circulated among the highest levels of the federal government and is used to determine daily priorities for the agencies working on a COVID-19 response, said 40 U.S. states and territories are in an upward trajectory of new infections, while nine jurisdictions are at a plateau and seven others are in a downward trend.

There were 488,498 new cases confirmed during the period of Oct. 19-25, a 26% increase from the previous week. There were also 5,615 fatalities from COVID-19 recorded during the same period, a 15.1% increase compared with the week prior, according to the memo.

The national positivity rate for COVID-19 tests increased from 5.6% to 6.1% in week-to-week comparisons. Meanwhile, 22% of hospitals across the country have intensive care units that are more than 80% occupied. That figure is up from the summertime peak, when 17-18% of U.S. hospitals had 80% of ICU beds full, the memo said.

Arizona reported 848 COVID-19 hospitalizations on Oct. 21, its highest count since Aug. 26, according to the memo.

In the U.S. territory of Guam, which continues to be classified as a "red zone" for COVID-19 infections, an average of 89.7% of inpatient beds and 80.2% of ICU beds were occupied in the week ending Oct. 20, the memo said.

North Dakota saw a record high of 1,036 new cases on Oct. 20, surpassing the 1,000 mark of daily incident cases for the first time, according to the memo.

New Jersey reported 852 daily COVID-19 hospitalizations on Oct. 22, its highest since late July, the memo said.

Oklahoma reached a record 956 COVID-19 hospitalizations on Oct. 22. The previous record was set just two days earlier, according to the memo.

Utah reported an all-time high of 314 COVID-19 hospitalizations on Oct. 21, as several hospitals in the state reached capacity, the memo said.

ABC News' Josh Margolin contributed to this report.