No country has formally recognised the Taliban government since the insurgents took over the country in August, while billions of dollars in Afghan assets and funds abroad have also been frozen, even as the country faces severe economic and humanitarian crises.
"Our message to America is, if unrecognition continues, Afghan problems continue, it is the problem of the region and could turn into a problem for the world," Taliban spokesman Zabihullah Mujahid told journalists at a news conference on Saturday.
He said the reason the Taliban and the United States went to war last time was also because the two did not have formal diplomatic ties.
The United States invaded Afghanistan in 2001 following the Sept 11, 2001, attack after the then-Taliban government refused to hand over al Qaeda chief Osama bin Laden.
"Those issues which caused the war, they could have been solved through negotiation, they could have been solved through political compromise too," Mujahid said.
He added that recognition was the right of the Afghan people.
While no country has recognised the Taliban government, senior officials from a number of countries have met with the movement's leadership both in Kabul and abroad.
The latest visit was by Turkmen Foreign Minister Rasit Meredow, who was in Kabul on Saturday. The two sides discussed the speedy implementation of the Turkmenistan-Afghanistan-Pakistan-India (TAPI) gas pipeline, Mujahid said earlier on Twitter.
China's foreign minister, Wang Yi, met Taliban officials in Qatar earlier this week. Mujahid said on Saturday that China had promised to finance transport infrastructure, and to give Kabul's exports access to Chinese markets via neighbouring Pakistan.
Mujahid also spoke at length about the issues facing border crossings, particularly with Pakistan, which have seen frequent closures and protests in recent days. The crossings are crucial for landlocked Afghanistan.
He said serious talks on the matter were held when Pakistan's foreign minister had travelled to Kabul last week.