The Taliban claimed control over two of Afghanistan's biggest cities on Thursday, according to media reports, as the United States and Britain said they would send thousands of troops to help evacuate their embassy staff, Reuters reported.

According to Reuters the capture of Kandahar and Herat - the country's second and third largest cities - would represent the Taliban's two biggest military victories since they began a broad offensive in May.

The fall of major cities was a sign that Afghans welcome the Taliban, a spokesperson for the group said, according to Al Jazeera TV.

The U.S. State Department said Secretary of State Antony Blinken and Defense Secretary Lloyd Austin spoke to Afghan President Ashraf Ghani on Thursday and told him the United States "remains invested in the security and stability of Afghanistan". They also said the United States was committed to supporting a political solution to the conflict.

In response to the Taliban's swift and violent advances, the Pentagon said it would send about 3,000 extra troops within 48 hours to help evacuate embassy staff, Reuters reported.

"We expect to draw down to a core diplomatic presence in Afghanistan in the coming weeks," said State Department spokesperson Ned Price, adding the embassy was not closed. A person familiar with the matter said there were no guarantees the embassy would remain open.

The State Department said it would also increase the tempo of Special Immigration Visa flights for Afghans who helped the U.S. effort in the country.

Britain said it would deploy around 600 troops to help its nationals and local translators get out.

According to Reuters as the United Nations warned that a Taliban offensive reaching the capital would have a "catastrophic impact on civilians," the United States and Germany urged all their citizens to leave Afghanistan immediately.

In Qatar, international envoys to Afghan negotiations called for an accelerated peace process as a "matter of great urgency," and for an immediate halt to attacks on cities.

The fall of both Kandahar and Herat was reported by media including the Associated Press. Combined, the cities represent the two biggest prizes yet for the Taliban in their offensive over the past week.

"As you can see, we are inside the Herat police headquarters right now," a Taliban fighter said in a video shared by a group spokesperson, Qari Yousuf Ahmadi.

Earlier on Thursday, the Taliban captured Ghazni, situated on the Kandahar-to-Kabul road some 150 km (90 miles) southwest of the capital, Reuters reported.

On the border, Afghans stranded in Pakistan after the Taliban closed a commercially vital crossing point clashed with Pakistani forces. The death of an Afghan traveller of a heart attack as he waited in the dusty heat near the Chaman-Spin Boldak crossing sparked an attack by others on Pakistani security forces, who responded by firing tear gas and charging with batons.

On Wednesday, a U.S. defense official cited U.S. intelligence as saying the Taliban could isolate Kabul in 30 days and possibly take it over within 90.

With phone lines down across much of the country, Reuters was unable to immediately contact government officials to confirm which of the cities under attack remained in government hands, Reuters reported.