All Senators will receive an unclassified virtual briefing on Afghanistan on Friday at 3:15 p.m., a Senate official told ABC News, as a bipartisan group of senators urges Biden to do more to evacuate Afghan allies.

Separately, House Speaker Nancy Pelosi has requested three briefings on Afghanistan in the coming days, a source familiar told ABC News, including an unclassified telephone briefing Friday for all members, a classified in-person briefing on Tuesday for all members and a "Gang of Eight" briefing.

Top Republican Leaders Kevin McCarthy and Mitch McConnell have also called on the Biden administration for a classified briefing with the “Gang of Eight,” -- which includes the top House and Senate leaders, including the heads of the intel committees in both the House and Senate.

-ABC News’ Trish Turner and Mariam Khan

Dozens of protesters, including many women, marched throughout Kabul on Thursday, parading the Afghan national flag through the streets on Afghanistan's Independence Day, days after the president fled the country and the Taliban seized control.

Taliban fighters have fired warning shots into the air to disperse the protests.

The national flag is now evolving into a symbol of both identity and resistance against the Taliban, who have a white flag, which has been displayed in towns across the country and at the Taliban's first press conference earlier this week.

While Thursday's protests aren’t mass in scale, they underline the challenges the Taliban face as they attempt to rule after Afghans have exercised new rights over the last 20 years.

There were also protests in several provinces on Wednesday, including in the eastern province of Jalalabad, where the Taliban flag was replaced with the Afghan national flag in a public square.

-ABC News' Guy Daives and Sohel Uddin

As the U.S. continues its evacuation efforts from Kabul, the president and vice president met with members of their national security team on Thursday "to discuss security, diplomatic, and intelligence updates in Afghanistan," a White House official said in a statement.

The group included Secretary of State Antony Blinken, Secretary of Defense Lloyd Austin, Chairman of the Joint Chiefs of Staff Gen. Mark Milley, National Security Advisor Jake Sullivan and other top officials.

"They discussed the status of operations at Hamid Karzai International Airport (HKIA), which continues to be secure and operational as a result of DOD's efforts; our efforts to evacuate U.S. citizens, Embassy personnel, SIV applicants and their families, and vulnerable Afghans as quickly as possible; and that every day we operate troops on the ground are at risk," the official said, backing up Biden's assertions to ABC's George Stephanopoulos that he is unwilling to put Americans in harm's way any longer than necessary.

The statement confirmed the Pentagon's reporting that it has evacuated 7,000 people since Saturday and 12,000 people from Afghanistan since the end of July.

The European Parliament Committee on Foreign Affairs held a virtual session on Afghanistan on Thursday at which the High Representative of the European Union for Foreign Affairs and Security Policy and Vice President of the European Commission Josep Borrell called the situation in Afghanistan "a catastrophe."

"Since Sunday, we are facing a new painful reality on the ground in Afghanistan," Borrell said.

"Let me speak clearly and bluntly. This is a catastrophe. This is a catastrophe for the Afghan people, for the West's values and credibility and for the development of international relations," he continued.

"Was it foreseeable? Was it preventable? In any case, it's a nightmare because -- you know -- even if tonight the first 106 members of our staff of the European Union delegations has landed in Madrid, we cannot take all Afghan people out of the country."

He said there are still 300 Afghan staffers of the European delegations blocked from reaching the airport and finding seats on some of the EU member states' flights out of Kabul.