AMNA NAWAZ: The day's other headlines begin in Washington, where lawmakers appear no closer to reopening the government as the shutdown approaches the one-week mark.

In the Oval Office this afternoon, President Trump suggested that he is open to speaking with Democrats on their biggest demand, health care subsidies.

DONALD TRUMP, President of the United States: Well, if we -- if we made the right deal, I'd make a deal, sure.

AMNA NAWAZ: Democrats insist that any funding bill must extend Affordable Care Act subsidies that are set to expire at the end of the yea.

But, earlier in the day, Speaker Mike Johnson held firm that Republicans won't negotiate health care matters until after the government reopens.

REP.

MIKE JOHNSON (R-LA): We need a handful of Democrats to stop the madness, reopen the government, so that we can get to these critical debates about the year-end policy decisions with regard to the further reforms to health care.

Plain and simple, that's where we are.

AMNA NAWAZ: This evening House Minority Leader Hakeem Jeffries called Mr.

Trump's comments interesting and added that Democrats remain open to negotiating with any Republicans, including the president.

On the first day of its new term, the Supreme Court rejected an appeal from Ghislaine Maxwell.

Lawyers for Jeffrey Epstein's longtime associate had argued that a plea deal should have shielded her from prosecution.

The court's decision means her only chance of early release would be clemency from President Trump.

She's currently serving a 20-year prison term.

Also today, the court declined to hear Missouri's bid to revive a law intended to negate federal gun regulations in the state.

They also brushed aside a lawsuit by far right influencer Laura Loomer against social media companies that removed her from their platforms.

And the court rejected an appeal by Live Nation in a consumer antitrust case related to ticket pricing.

French Prime Minister Sebastien Lecornu resigned just a day after announcing his Cabinet and less than a month in office.

His Cabinet selections had faced criticism from allies and opponents alike.

Lecornu's announcement adds to ongoing political uncertainty in France after President Emmanuel Macron's decision last year to hold snap elections that left the legislature deeply divided.

It's now up to Macron whether to name a new prime minister or dissolve the National Assembly and call early elections.

Lecornu's government will manage day-to-day affairs in the meantime.

Israeli authorities say they have deported more than 170 activists who took part in a flotilla aiming to bring aid to Gaza.

Climate activist Greta Thunberg was among the dozens who landed in Athens earlier today.

Israel also denied accusations that the activists had been mistreated while in Israeli custody.

Israel's Foreign Ministry posted images of their release, writing that -- quote -- "All the legal rights of the participants in this P.R.

stunt were and will continue to be fully upheld."

Meanwhile, lawyers say at least 150 people are still being held in Israel, with dozens taking part in a hunger strike.

The International Criminal Court today convicted a Janjaweed militia leader for atrocities committed in Sudan's Darfur region more than two decades ago.

JOANNA KORNER, Presiding Judge, International Criminal Court: The chamber is convinced that the accused is guilty beyond reasonable doubt of the crimes with which he has been charged.

AMNA NAWAZ: Ali Muhammad Ali Abd-Al-Rahman showed little emotion as he was found guilty on 27 counts of crimes against humanity and war crimes.

He had denied the charges.

It is the first such conviction related to the violence in Darfur, where up to 300,000 people were killed and millions driven from their homes during a government crackdown on a rebellion starting in 2003.

Abd-Al-Rahman faces a maximum sentence of life in prison.

In Tibet, a rescue has been taking place on Mount Everest, where hundreds of hikers were trapped by heavy snow.

Chinese state media reported that around 350 hikers had made their way down to a safe meeting point, while rescuers are in contact with 200 others still on the mountain.

The hikers were stranded at an elevation of more than 16,000 feet.

The snowstorm hit during a weeklong national holiday in China, when many people travel both within China and abroad.

Mount Everest has seen multiple accidents and overcrowding issues in recent years.

Back in this country, South Carolina's top law official says there's no evidence to suggest that arson was to blame for a fire that destroyed a circuit court judge's home over the weekend, though the investigation is ongoing.

Smoke billowed over the marshes of Edisto Island as the residents went up in flames on Saturday.

Officials say three people were injured, but did not provide details.

The property is owned by circuit Judge Diane Goodstein, who has been a state judge for nearly three decades.

Last month, she temporarily blocked South Carolina from giving state voter data to the Department of Justice.

The CDC officially updated its vaccine guidelines today to align with recommendations made by the advisory committee that was picked by Health Secretary Robert F. Kennedy Jr.

The agency is no longer recommending COVID-19 vaccines for all Americans 6 months and older.

Instead, officials are encouraging -- quote -- "individual-based decision-making."

That includes checking with a medical professional, especially for seniors.

The agency is also recommending a stand-alone chicken pox shot for toddlers, rather than combining it with measles, mumps and rubella.

Many medical experts warn the committee's recommendations have led to confusion and mistrust over vaccines.

On Wall Street today, stocks started the week mixed.

The Dow Jones industrial average slipped about 60 points.

The Nasdaq rose around 160 points.

The S&P 500 also ended in positive territory.

And a trio of scientists won this year's Nobel Prize in physiology or medicine for their work on the human immune system.

The committee said the discoveries of Mary Brunkow, Fred Ramsdell and Shimon Sakaguchi helped advance treatments for cancer and autoimmune diseases and could help with organ transplants.

The announcement today in Sweden was the first of this year's Nobel announcements.

The three will share nearly $1.2 million in prize money.

And, tomorrow, the physics prize will be handed out.

Still to come on the "News Hour": why an increasing number of Israeli Reservists are refusing to be redeployed to Gaza; a leadership change shakes up CBS News; and Tamara Keith and Amy Walter discuss the state of the government shutdown.