Zalmay Khalilzad is on a 17-day trip that will also take him to Afghanistan, Pakistan, Germany, Belgium and the United Arab Emirates.
Mullah Haibatullah Akhundzada also gives no sign the Taliban will repeat last year's truce over the three-day Eid holiday.
Hamid Karzai's announcement unleashed a brief spell of confusion across the country.
The blast comes one day after an Islamic State suicide bomber blew himself up outside an Afghan army military academy, killing at least six people.
Lindh, 38, is a free man now after his release from high-security prison in Terre Haute, Indiana three years early for good behaviour in a 20-year sentence.
Kemajuan rundingan AS-Taliban agak perlahan, manakala butirannya kekal kabur.
The attack comes as the US and Taliban representatives continue negotiations in Qatar aimed at bringing an end to the nearly 18-year-old conflict.
Both parties have spent much of the past week in a sixth round of talks in Doha aimed at ending America's longest war.
The suicide bomber blows himself up in a Humvee filled with explosives followed by the emergence of other fighters opening fire outside a police headquarters.
Pertempuran tercetus di wilayah Nangarhar apabila militan IS menyerang perkampungan bawah kawalan Taliban.
The majority of the deaths resulted from US air strikes or from search operations on the ground, primarily conducted by US-backed Afghan forces.
A planned peace summit in Doha has been postponed as the Taliban questions the number of delegates Kabul was to send.
The Taliban – who see Ghani as a US stooge and his government as a puppet regime – also insisted they would not be negotiating with Kabul at the conference.
John Walker Lindh will also not be allowed to travel abroad for the three years without express court permission.
Militan Taliban berjaya menguasai daerah Ab Kamari pada lewat malam Jumaat selepas 3 hari mengepungnya.
"Some were against this concert, but we did not give up," she said. "We are all scared of suicide bombings, explosions, abductions and other issues in this country."
The Rembau MP says the Umno-PAS alliance will never lead to Malaysia being run like the Taliban rule in Afghanistan.
Pengerusi DAP Perak, Nga Kor Ming sebelum ini dilaporkan berkata, kerjasama PAS dan Umno akan membawa negara ke arah pemerintahan ala Taliban.
Taliban rule had kept women in the kitchen and homes and deprived them of a future, Zahra Elham's 'Afghan Star' win is a statement of empowerment for women in Afghanistan.
Umno MP says if his use of the word ‘Taliban’ is an insult to Parliament, then Nga Kor Ming is equally guilty.
Ahli Parlimen Rembau itu berkata demikian ketika bertanya kerajaan PH sama ada ia akan mencontohi BN memberi bantuan RM450 kepada orang bujang dalam kumpulan B40 selepas PRK Rantau.
The Rembau MP said this when asking if the Pakatan Harapan government would emulate Barisan Nasional in giving RM450 to single people in the B40 group after the Rantau by-election.
Afghanistan's multi-day celebrations to mark its traditional new year have been marred by several attacks.
The casualties from the second blast had been minimal as people fled the area after the first.