New COVID-19 cases in the U.S. are seeing a "very encouraging" drop, according to The COVID Tracking Project.

The number of weekly cases decreased 21% as of Saturday, the tracker said. There were "more modest but very welcome" drops in COVID-19 deaths and hospitalizations as well.

The seven-day average for cases is back to "pre-Thanksgiving levels," though the group noted there are still nearly three times as many new cases daily compared to the summer peak.

Los Angeles County has crossed 15,000 deaths, with about one-third of those deaths happening in 2021.

Health officials reported 269 deaths in the county on Saturday. LA remains the hardest-hit county in the United States. LA County has more than twice as many cases (1,064,887) as the second-highest in the nation (Arizona's Maricopa County; 444,431, according to Johns Hopkins University).

The county said 5,106 people have died since Dec. 30.

There was a little bit of good news in LA, however, as the county is following national trends of dropping hospitalizations. The number of people in hospitals with COVID-19 dropped under 7,000 for the first time since Dec. 29, according to the health department.

"Many people continue to spread this virus and, tragically, now more than 15,000 people have died from COVID-19 in Los Angeles County," Dr. Barbara Ferrer, the county's director of public health, said in a statement. "While we are seeing some positive data in daily new cases and hospitalizations, we are far from out of the woods. It is critically important we slow COVID-19 spread to decompress the strain on our healthcare system and save lives."

ABC News' Matthew Fuhrman contributed to this report.

Week-to-week comparisons show new deaths and new cases are on the decline nationwide, according to an internal Department of Health and Human Services memo obtained by ABC News.

Thirty-one states and territories are in a downward trajectory of new cases, according to the memo. Twenty states and territories are in an upward trajectory of new cases while five jurisdictions are at a plateau.

The U.S. saw 1,318,915 new cases from Jan. 16 to Jan. 22 -- a 20.3% decrease from the previous week.

There were 21,442 deaths reported from Jan. 16 to Jan. 22, which was a 7.7% decrease from the week before.

The national test-positivity rate also dropped, falling from 11.9% to 10.4% in week-to-week comparisons, the memo said.

ABC News’ Josh Margolin contributed to this report.

Indoor dining resumed in Chicago on Saturday as the city moved to “Tier 1” of reopening “due to recent progress in the fight against COVID-19,” Mayor Lori Lightfoot said.

Indoor dining is limited to 25 people or 25% capacity with tables six feet apart.

All bars and restaurants must close at 11 p.m.

"We have long pushed for the careful resumption of limited indoor dining, and I am thrilled that we have made enough progress … to reopen our businesses and bring workers back," Lightfoot said in a statement, according to ABC Chicago station WLS.

Twenty-three reports of suspected deaths associated with COVID-19 vaccines have been submitted to Norway's national health registry as of Jan. 14, according to an updated statement from the country's drug regulator on Monday.

The Norwegian Medicines Agency said it "cannot rule out that adverse reactions to the vaccine occurring within the first days following vaccination (such as fever and nausea) may contribute to more serious course and fatal outcome in patients with severe underlying disease."

Thirteen of those reports have been assessed by the drug regulator, as well as the Norwegian Institute of Public Health.

"The reports suggest that common adverse reactions to mRNA vaccines, such as fever and nausea, may have contributed to a fatal outcome in some frail patients," Sigurd Hortemo, chief physician at the Norwegian Medicines Agency, said in the statement.

Steinar Madsen, medical director of the Norwegian Medicines Agency, told the state-run broadcaster NRK: "We are not alarmed by this."

"It is quite clear that these vaccines have very little risk, with a small exception for the frailest patients," Madsen said. "Doctors must now carefully consider who should be vaccinated. Those who are very frail and at the very end of life can be vaccinated after an individual assessment."

Norway is currently administering COVID-19 vaccines to the elderly and people in nursing homes with serious underlying diseases -- at first with just the Pfizer/BioNTech vaccine up until Jan. 15, and then also with the Moderna vaccine. Official figures show that more than 30,000 people have received the first shot of the Pfizer or Moderna vaccines in Norway since the end of December.

According to the Norwegian Medicines Agency, an average of 400 people die each week in nursing homes and long-term care facilities nationwide.

The Scandinavian country of 5.3 million people has confirmed more than 58,000 cases of COVID-19 since the start of the pandemic, including at least 521 deaths, according to the latest data from the Norwegian Institute of Public Health.